var bigInt = (function (undefined) {
"use strict";
var BASE = 1e7,
LOG_BASE = 7,
MAX_INT = 9007199254740992,
MAX_INT_ARR = smallToArray(MAX_INT),
LOG_MAX_INT = Math.log(MAX_INT);
function Integer(v, radix) {
if (typeof v === "undefined") return Integer[0];
if (typeof radix !== "undefined") return +radix === 10 ? parseValue(v) : parseBase(v, radix);
return parseValue(v);
}
function BigInteger(value, sign) {
this.value = value;
this.sign = sign;
this.isSmall = false;
}
BigInteger.prototype = Object.create(Integer.prototype);
function SmallInteger(value) {
this.value = value;
this.sign = value < 0;
this.isSmall = true;
}
SmallInteger.prototype = Object.create(Integer.prototype);
function isPrecise(n) {
return -MAX_INT < n && n < MAX_INT;
}
function smallToArray(n) { // For performance reasons doesn't reference BASE, need to change this function if BASE changes
if (n < 1e7)
return [n];
if (n < 1e14)
return [n % 1e7, Math.floor(n / 1e7)];
return [n % 1e7, Math.floor(n / 1e7) % 1e7, Math.floor(n / 1e14)];
}
function arrayToSmall(arr) { // If BASE changes this function may need to change
trim(arr);
var length = arr.length;
if (length < 4 && compareAbs(arr, MAX_INT_ARR) < 0) {
switch (length) {
case 0: return 0;
case 1: return arr[0];
case 2: return arr[0] + arr[1] * BASE;
default: return arr[0] + (arr[1] + arr[2] * BASE) * BASE;
}
}
return arr;
}
function trim(v) {
var i = v.length;
while (v[--i] === 0);
v.length = i + 1;
}
function createArray(length) { // function shamelessly stolen from Yaffle's library https://github.com/Yaffle/BigInteger
var x = new Array(length);
var i = -1;
while (++i < length) {
x[i] = 0;
}
return x;
}
function truncate(n) {
if (n > 0) return Math.floor(n);
return Math.ceil(n);
}
function add(a, b) { // assumes a and b are arrays with a.length >= b.length
var l_a = a.length,
l_b = b.length,
r = new Array(l_a),
carry = 0,
base = BASE,
sum, i;
for (i = 0; i < l_b; i++) {
sum = a[i] + b[i] + carry;
carry = sum >= base ? 1 : 0;
r[i] = sum - carry * base;
}
while (i < l_a) {
sum = a[i] + carry;
carry = sum === base ? 1 : 0;
r[i++] = sum - carry * base;
}
if (carry > 0) r.push(carry);
return r;
}
function addAny(a, b) {
if (a.length >= b.length) return add(a, b);
return add(b, a);
}
function addSmall(a, carry) { // assumes a is array, carry is number with 0 <= carry < MAX_INT
var l = a.length,
r = new Array(l),
base = BASE,
sum, i;
for (i = 0; i < l; i++) {
sum = a[i] - base + carry;
carry = Math.floor(sum / base);
r[i] = sum - carry * base;
carry += 1;
}
while (carry > 0) {
r[i++] = carry % base;
carry = Math.floor(carry / base);
}
return r;
}
BigInteger.prototype.add = function (v) {
var value, n = parseValue(v);
if (this.sign !== n.sign) {
return this.subtract(n.negate());
}
var a = this.value, b = n.value;
if (n.isSmall) {
return new BigInteger(addSmall(a, Math.abs(b)), this.sign);
}
return new BigInteger(addAny(a, b), this.sign);
};
BigInteger.prototype.plus = BigInteger.prototype.add;
SmallInteger.prototype.add = function (v) {
var n = parseValue(v);
var a = this.value;
if (a < 0 !== n.sign) {
return this.subtract(n.negate());
}
var b = n.value;
if (n.isSmall) {
if (isPrecise(a + b)) return new SmallInteger(a + b);
b = smallToArray(Math.abs(b));
}
return new BigInteger(addSmall(b, Math.abs(a)), a < 0);
};
SmallInteger.prototype.plus = SmallInteger.prototype.add;
function subtract(a, b) { // assumes a and b are arrays with a >= b
var a_l = a.length,
b_l = b.length,
r = new Array(a_l),
borrow = 0,
base = BASE,
i, difference;
for (i = 0; i < b_l; i++) {
difference = a[i] - borrow - b[i];
if (difference < 0) {
difference += base;
borrow = 1;
} else borrow = 0;
r[i] = difference;
}
for (i = b_l; i < a_l; i++) {
difference = a[i] - borrow;
if (difference < 0) difference += base;
else {
r[i++] = difference;
break;
}
r[i] = difference;
}
for (; i < a_l; i++) {
r[i] = a[i];
}
trim(r);
return r;
}
function subtractAny(a, b, sign) {
var value, isSmall;
if (compareAbs(a, b) >= 0) {
value = subtract(a,b);
} else {
value = subtract(b, a);
sign = !sign;
}
value = arrayToSmall(value);
if (typeof value === "number") {
if (sign) value = -value;
return new SmallInteger(value);
}
return new BigInteger(value, sign);
}
function subtractSmall(a, b, sign) { // assumes a is array, b is number with 0 <= b < MAX_INT
var l = a.length,
r = new Array(l),
carry = -b,
base = BASE,
i, difference;
for (i = 0; i < l; i++) {
difference = a[i] + carry;
carry = Math.floor(difference / base);
difference %= base;
r[i] = difference < 0 ? difference + base : difference;
}
r = arrayToSmall(r);
if (typeof r === "number") {
if (sign) r = -r;
return new SmallInteger(r);
} return new BigInteger(r, sign);
}
BigInteger.prototype.subtract = function (v) {
var n = parseValue(v);
if (this.sign !== n.sign) {
return this.add(n.negate());
}
var a = this.value, b = n.value;
if (n.isSmall)
return subtractSmall(a, Math.abs(b), this.sign);
return subtractAny(a, b, this.sign);
};
BigInteger.prototype.minus = BigInteger.prototype.subtract;
SmallInteger.prototype.subtract = function (v) {
var n = parseValue(v);
var a = this.value;
if (a < 0 !== n.sign) {
return this.add(n.negate());
}
var b = n.value;
if (n.isSmall) {
return new SmallInteger(a - b);
}
return subtractSmall(b, Math.abs(a), a >= 0);
};
SmallInteger.prototype.minus = SmallInteger.prototype.subtract;
BigInteger.prototype.negate = function () {
return new BigInteger(this.value, !this.sign);
};
SmallInteger.prototype.negate = function () {
var sign = this.sign;
var small = new SmallInteger(-this.value);
small.sign = !sign;
return small;
};
BigInteger.prototype.abs = function () {
return new BigInteger(this.value, false);
};
SmallInteger.prototype.abs = function () {
return new SmallInteger(Math.abs(this.value));
};
function multiplyLong(a, b) {
var a_l = a.length,
b_l = b.length,
l = a_l + b_l,
r = createArray(l),
base = BASE,
product, carry, i, a_i, b_j;
for (i = 0; i < a_l; ++i) {
a_i = a[i];
for (var j = 0; j < b_l; ++j) {
b_j = b[j];
product = a_i * b_j + r[i + j];
carry = Math.floor(product / base);
r[i + j] = product - carry * base;
r[i + j + 1] += carry;
}
}
trim(r);
return r;
}
function multiplySmall(a, b) { // assumes a is array, b is number with |b| < BASE
var l = a.length,
r = new Array(l),
base = BASE,
carry = 0,
product, i;
for (i = 0; i < l; i++) {
product = a[i] * b + carry;
carry = Math.floor(product / base);
r[i] = product - carry * base;
}
while (carry > 0) {
r[i++] = carry % base;
carry = Math.floor(carry / base);
}
return r;
}
function shiftLeft(x, n) {
var r = [];
while (n-- > 0) r.push(0);
return r.concat(x);
}
function multiplyKaratsuba(x, y) {
var n = Math.max(x.length, y.length);
if (n <= 30) return multiplyLong(x, y);
n = Math.ceil(n / 2);
var b = x.slice(n),
a = x.slice(0, n),
d = y.slice(n),
c = y.slice(0, n);
var ac = multiplyKaratsuba(a, c),
bd = multiplyKaratsuba(b, d),
abcd = multiplyKaratsuba(addAny(a, b), addAny(c, d));
var product = addAny(addAny(ac, shiftLeft(subtract(subtract(abcd, ac), bd), n)), shiftLeft(bd, 2 * n));
trim(product);
return product;
}
// The following function is derived from a surface fit of a graph plotting the performance difference
// between long multiplication and karatsuba multiplication versus the lengths of the two arrays.
function useKaratsuba(l1, l2) {
return -0.012 * l1 - 0.012 * l2 + 0.000015 * l1 * l2 > 0;
}
BigInteger.prototype.multiply = function (v) {
var value, n = parseValue(v),
a = this.value, b = n.value,
sign = this.sign !== n.sign,
abs;
if (n.isSmall) {
if (b === 0) return Integer[0];
if (b === 1) return this;
if (b === -1) return this.negate();
abs = Math.abs(b);
if (abs < BASE) {
return new BigInteger(multiplySmall(a, abs), sign);
}
b = smallToArray(abs);
}
if (useKaratsuba(a.length, b.length)) // Karatsuba is only faster for certain array sizes
return new BigInteger(multiplyKaratsuba(a, b), sign);
return new BigInteger(multiplyLong(a, b), sign);
};
BigInteger.prototype.times = BigInteger.prototype.multiply;
function multiplySmallAndArray(a, b, sign) { // a >= 0
if (a < BASE) {
return new BigInteger(multiplySmall(b, a), sign);
}
return new BigInteger(multiplyLong(b, smallToArray(a)), sign);
}
SmallInteger.prototype._multiplyBySmall = function (a) {
if (isPrecise(a.value * this.value)) {
return new SmallInteger(a.value * this.value);
}
return multiplySmallAndArray(Math.abs(a.value), smallToArray(Math.abs(this.value)), this.sign !== a.sign);
};
BigInteger.prototype._multiplyBySmall = function (a) {
if (a.value === 0) return Integer[0];
if (a.value === 1) return this;
if (a.value === -1) return this.negate();
return multiplySmallAndArray(Math.abs(a.value), this.value, this.sign !== a.sign);
};
SmallInteger.prototype.multiply = function (v) {
return parseValue(v)._multiplyBySmall(this);
};
SmallInteger.prototype.times = SmallInteger.prototype.multiply;
function square(a) {
var l = a.length,
r = createArray(l + l),
base = BASE,
product, carry, i, a_i, a_j;
for (i = 0; i < l; i++) {
a_i = a[i];
for (var j = 0; j < l; j++) {
a_j = a[j];
product = a_i * a_j + r[i + j];
carry = Math.floor(product / base);
r[i + j] = product - carry * base;
r[i + j + 1] += carry;
}
}
trim(r);
return r;
}
BigInteger.prototype.square = function () {
return new BigInteger(square(this.value), false);
};
SmallInteger.prototype.square = function () {
var value = this.value * this.value;
if (isPrecise(value)) return new SmallInteger(value);
return new BigInteger(square(smallToArray(Math.abs(this.value))), false);
};
function divMod1(a, b) { // Left over from previous version. Performs faster than divMod2 on smaller input sizes.
var a_l = a.length,
b_l = b.length,
base = BASE,
result = createArray(b.length),
divisorMostSignificantDigit = b[b_l - 1],
// normalization
lambda = Math.ceil(base / (2 * divisorMostSignificantDigit)),
remainder = multiplySmall(a, lambda),
divisor = multiplySmall(b, lambda),
quotientDigit, shift, carry, borrow, i, l, q;
if (remainder.length <= a_l) remainder.push(0);
divisor.push(0);
divisorMostSignificantDigit = divisor[b_l - 1];
for (shift = a_l - b_l; shift >= 0; shift--) {
quotientDigit = base - 1;
if (remainder[shift + b_l] !== divisorMostSignificantDigit) {
quotientDigit = Math.floor((remainder[shift + b_l] * base + remainder[shift + b_l - 1]) / divisorMostSignificantDigit);
}
// quotientDigit <= base - 1
carry = 0;
borrow = 0;
l = divisor.length;
for (i = 0; i < l; i++) {
carry += quotientDigit * divisor[i];
q = Math.floor(carry / base);
borrow += remainder[shift + i] - (carry - q * base);
carry = q;
if (borrow < 0) {
remainder[shift + i] = borrow + base;
borrow = -1;
} else {
remainder[shift + i] = borrow;
borrow = 0;
}
}
while (borrow !== 0) {
quotientDigit -= 1;
carry = 0;
for (i = 0; i < l; i++) {
carry += remainder[shift + i] - base + divisor[i];
if (carry < 0) {
remainder[shift + i] = carry + base;
carry = 0;
} else {
remainder[shift + i] = carry;
carry = 1;
}
}
borrow += carry;
}
result[shift] = quotientDigit;
}
// denormalization
remainder = divModSmall(remainder, lambda)[0];
return [arrayToSmall(result), arrayToSmall(remainder)];
}
function divMod2(a, b) { // Implementation idea shamelessly stolen from Silent Matt's library http://silentmatt.com/biginteger/
// Performs faster than divMod1 on larger input sizes.
var a_l = a.length,
b_l = b.length,
result = [],
part = [],
base = BASE,
guess, xlen, highx, highy, check;
while (a_l) {
part.unshift(a[--a_l]);
if (compareAbs(part, b) < 0) {
result.push(0);
continue;
}
xlen = part.length;
highx = part[xlen - 1] * base + part[xlen - 2];
highy = b[b_l - 1] * base + b[b_l - 2];
if (xlen > b_l) {
highx = (highx + 1) * base;
}
guess = Math.ceil(highx / highy);
do {
check = multiplySmall(b, guess);
if (compareAbs(check, part) <= 0) break;
guess--;
} while (guess);
result.push(guess);
part = subtract(part, check);
}
result.reverse();
return [arrayToSmall(result), arrayToSmall(part)];
}
function divModSmall(value, lambda) {
var length = value.length,
quotient = createArray(length),
base = BASE,
i, q, remainder, divisor;
remainder = 0;
for (i = length - 1; i >= 0; --i) {
divisor = remainder * base + value[i];
q = truncate(divisor / lambda);
remainder = divisor - q * lambda;
quotient[i] = q | 0;
}
return [quotient, remainder | 0];
}
function divModAny(self, v) {
var value, n = parseValue(v);
var a = self.value, b = n.value;
var quotient;
if (b === 0) throw new Error("Cannot divide by zero");
if (self.isSmall) {
if (n.isSmall) {
return [new SmallInteger(truncate(a / b)), new SmallInteger(a % b)];
}
return [Integer[0], self];
}
if (n.isSmall) {
if (b === 1) return [self, Integer[0]];
if (b == -1) return [self.negate(), Integer[0]];
var abs = Math.abs(b);
if (abs < BASE) {
value = divModSmall(a, abs);
quotient = arrayToSmall(value[0]);
var remainder = value[1];
if (self.sign) remainder = -remainder;
if (typeof quotient === "number") {
if (self.sign !== n.sign) quotient = -quotient;
return [new SmallInteger(quotient), new SmallInteger(remainder)];
}
return [new BigInteger(quotient, self.sign !== n.sign), new SmallInteger(remainder)];
}
b = smallToArray(abs);
}
var comparison = compareAbs(a, b);
if (comparison === -1) return [Integer[0], self];
if (comparison === 0) return [Integer[self.sign === n.sign ? 1 : -1], Integer[0]];
// divMod1 is faster on smaller input sizes
if (a.length + b.length <= 200)
value = divMod1(a, b);
else value = divMod2(a, b);
quotient = value[0];
var qSign = self.sign !== n.sign,
mod = value[1],
mSign = self.sign;
if (typeof quotient === "number") {
if (qSign) quotient = -quotient;
quotient = new SmallInteger(quotient);
} else quotient = new BigInteger(quotient, qSign);
if (typeof mod === "number") {
if (mSign) mod = -mod;
mod = new SmallInteger(mod);
} else mod = new BigInteger(mod, mSign);
return [quotient, mod];
}
BigInteger.prototype.divmod = function (v) {
var result = divModAny(this, v);
return {
quotient: result[0],
remainder: result[1]
};
};
SmallInteger.prototype.divmod = BigInteger.prototype.divmod;
BigInteger.prototype.divide = function (v) {
return divModAny(this, v)[0];
};
SmallInteger.prototype.over = SmallInteger.prototype.divide = BigInteger.prototype.over = BigInteger.prototype.divide;
BigInteger.prototype.mod = function (v) {
return divModAny(this, v)[1];
};
SmallInteger.prototype.remainder = SmallInteger.prototype.mod = BigInteger.prototype.remainder = BigInteger.prototype.mod;
BigInteger.prototype.pow = function (v) {
var n = parseValue(v),
a = this.value,
b = n.value,
value, x, y;
if (b === 0) return Integer[1];
if (a === 0) return Integer[0];
if (a === 1) return Integer[1];
if (a === -1) return n.isEven() ? Integer[1] : Integer[-1];
if (n.sign) {
return Integer[0];
}
if (!n.isSmall) throw new Error("The exponent " + n.toString() + " is too large.");
if (this.isSmall) {
if (isPrecise(value = Math.pow(a, b)))
return new SmallInteger(truncate(value));
}
x = this;
y = Integer[1];
while (true) {
if (b & 1 === 1) {
y = y.times(x);
--b;
}
if (b === 0) break;
b /= 2;
x = x.square();
}
return y;
};
SmallInteger.prototype.pow = BigInteger.prototype.pow;
BigInteger.prototype.modPow = function (exp, mod) {
exp = parseValue(exp);
mod = parseValue(mod);
if (mod.isZero()) throw new Error("Cannot take modPow with modulus 0");
var r = Integer[1],
base = this.mod(mod);
while (exp.isPositive()) {
if (base.isZero()) return Integer[0];
if (exp.isOdd()) r = r.multiply(base).mod(mod);
exp = exp.divide(2);
base = base.square().mod(mod);
}
return r;
};
SmallInteger.prototype.modPow = BigInteger.prototype.modPow;
function compareAbs(a, b) {
if (a.length !== b.length) {
return a.length > b.length ? 1 : -1;
}
for (var i = a.length - 1; i >= 0; i--) {
if (a[i] !== b[i]) return a[i] > b[i] ? 1 : -1;
}
return 0;
}
BigInteger.prototype.compareAbs = function (v) {
var n = parseValue(v),
a = this.value,
b = n.value;
if (n.isSmall) return 1;
return compareAbs(a, b);
};
SmallInteger.prototype.compareAbs = function (v) {
var n = parseValue(v),
a = Math.abs(this.value),
b = n.value;
if (n.isSmall) {
b = Math.abs(b);
return a === b ? 0 : a > b ? 1 : -1;
}
return -1;
};
BigInteger.prototype.compare = function (v) {
// See discussion about comparison with Infinity:
// https://github.com/peterolson/BigInteger.js/issues/61
if (v === Infinity) {
return -1;
}
if (v === -Infinity) {
return 1;
}
var n = parseValue(v),
a = this.value,
b = n.value;
if (this.sign !== n.sign) {
return n.sign ? 1 : -1;
}
if (n.isSmall) {
return this.sign ? -1 : 1;
}
return compareAbs(a, b) * (this.sign ? -1 : 1);
};
BigInteger.prototype.compareTo = BigInteger.prototype.compare;
SmallInteger.prototype.compare = function (v) {
if (v === Infinity) {
return -1;
}
if (v === -Infinity) {
return 1;
}
var n = parseValue(v),
a = this.value,
b = n.value;
if (n.isSmall) {
return a == b ? 0 : a > b ? 1 : -1;
}
if (a < 0 !== n.sign) {
return a < 0 ? -1 : 1;
}
return a < 0 ? 1 : -1;
};
SmallInteger.prototype.compareTo = SmallInteger.prototype.compare;
BigInteger.prototype.equals = function (v) {
return this.compare(v) === 0;
};
SmallInteger.prototype.eq = SmallInteger.prototype.equals = BigInteger.prototype.eq = BigInteger.prototype.equals;
BigInteger.prototype.notEquals = function (v) {
return this.compare(v) !== 0;
};
SmallInteger.prototype.neq = SmallInteger.prototype.notEquals = BigInteger.prototype.neq = BigInteger.prototype.notEquals;
BigInteger.prototype.greater = function (v) {
return this.compare(v) > 0;
};
SmallInteger.prototype.gt = SmallInteger.prototype.greater = BigInteger.prototype.gt = BigInteger.prototype.greater;
BigInteger.prototype.lesser = function (v) {
return this.compare(v) < 0;
};
SmallInteger.prototype.lt = SmallInteger.prototype.lesser = BigInteger.prototype.lt = BigInteger.prototype.lesser;
BigInteger.prototype.greaterOrEquals = function (v) {
return this.compare(v) >= 0;
};
SmallInteger.prototype.geq = SmallInteger.prototype.greaterOrEquals = BigInteger.prototype.geq = BigInteger.prototype.greaterOrEquals;
BigInteger.prototype.lesserOrEquals = function (v) {
return this.compare(v) <= 0;
};
SmallInteger.prototype.leq = SmallInteger.prototype.lesserOrEquals = BigInteger.prototype.leq = BigInteger.prototype.lesserOrEquals;
BigInteger.prototype.isEven = function () {
return (this.value[0] & 1) === 0;
};
SmallInteger.prototype.isEven = function () {
return (this.value & 1) === 0;
};
BigInteger.prototype.isOdd = function () {
return (this.value[0] & 1) === 1;
};
SmallInteger.prototype.isOdd = function () {
return (this.value & 1) === 1;
};
BigInteger.prototype.isPositive = function () {
return !this.sign;
};
SmallInteger.prototype.isPositive = function () {
return this.value > 0;
};
BigInteger.prototype.isNegative = function () {
return this.sign;
};
SmallInteger.prototype.isNegative = function () {
return this.value < 0;
};
BigInteger.prototype.isUnit = function () {
return false;
};
SmallInteger.prototype.isUnit = function () {
return Math.abs(this.value) === 1;
};
BigInteger.prototype.isZero = function () {
return false;
};
SmallInteger.prototype.isZero = function () {
return this.value === 0;
};
BigInteger.prototype.isDivisibleBy = function (v) {
var n = parseValue(v);
var value = n.value;
if (value === 0) return false;
if (value === 1) return true;
if (value === 2) return this.isEven();
return this.mod(n).equals(Integer[0]);
};
SmallInteger.prototype.isDivisibleBy = BigInteger.prototype.isDivisibleBy;
function isBasicPrime(v) {
var n = v.abs();
if (n.isUnit()) return false;
if (n.equals(2) || n.equals(3) || n.equals(5)) return true;
if (n.isEven() || n.isDivisibleBy(3) || n.isDivisibleBy(5)) return false;
if (n.lesser(25)) return true;
// we don't know if it's prime: let the other functions figure it out
}
BigInteger.prototype.isPrime = function () {
var isPrime = isBasicPrime(this);
if (isPrime !== undefined) return isPrime;
var n = this.abs(),
nPrev = n.prev();
var a = [2, 3, 5, 7, 11, 13, 17, 19],
b = nPrev,
d, t, i, x;
while (b.isEven()) b = b.divide(2);
for (i = 0; i < a.length; i++) {
x = bigInt(a[i]).modPow(b, n);
if (x.equals(Integer[1]) || x.equals(nPrev)) continue;
for (t = true, d = b; t && d.lesser(nPrev) ; d = d.multiply(2)) {
x = x.square().mod(n);
if (x.equals(nPrev)) t = false;
}
if (t) return false;
}
return true;
};
SmallInteger.prototype.isPrime = BigInteger.prototype.isPrime;
BigInteger.prototype.isProbablePrime = function (iterations) {
var isPrime = isBasicPrime(this);
if (isPrime !== undefined) return isPrime;
var n = this.abs();
var t = iterations === undefined ? 5 : iterations;
// use the Fermat primality test
for (var i = 0; i < t; i++) {
var a = bigInt.randBetween(2, n.minus(2));
if (!a.modPow(n.prev(), n).isUnit()) return false; // definitely composite
}
return true; // large chance of being prime
};
SmallInteger.prototype.isProbablePrime = BigInteger.prototype.isProbablePrime;
BigInteger.prototype.next = function () {
var value = this.value;
if (this.sign) {
return subtractSmall(value, 1, this.sign);
}
return new BigInteger(addSmall(value, 1), this.sign);
};
SmallInteger.prototype.next = function () {
var value = this.value;
if (value + 1 < MAX_INT) return new SmallInteger(value + 1);
return new BigInteger(MAX_INT_ARR, false);
};
BigInteger.prototype.prev = function () {
var value = this.value;
if (this.sign) {
return new BigInteger(addSmall(value, 1), true);
}
return subtractSmall(value, 1, this.sign);
};
SmallInteger.prototype.prev = function () {
var value = this.value;
if (value - 1 > -MAX_INT) return new SmallInteger(value - 1);
return new BigInteger(MAX_INT_ARR, true);
};
var powersOfTwo = [1];
while (powersOfTwo[powersOfTwo.length - 1] <= BASE) powersOfTwo.push(2 * powersOfTwo[powersOfTwo.length - 1]);
var powers2Length = powersOfTwo.length, highestPower2 = powersOfTwo[powers2Length - 1];
function shift_isSmall(n) {
return ((typeof n === "number" || typeof n === "string") && +Math.abs(n) <= BASE) ||
(n instanceof BigInteger && n.value.length <= 1);
}
BigInteger.prototype.shiftLeft = function (n) {
if (!shift_isSmall(n)) {
throw new Error(String(n) + " is too large for shifting.");
}
n = +n;
if (n < 0) return this.shiftRight(-n);
var result = this;
while (n >= powers2Length) {
result = result.multiply(highestPower2);
n -= powers2Length - 1;
}
return result.multiply(powersOfTwo[n]);
};
SmallInteger.prototype.shiftLeft = BigInteger.prototype.shiftLeft;
BigInteger.prototype.shiftRight = function (n) {
var remQuo;
if (!shift_isSmall(n)) {
throw new Error(String(n) + " is too large for shifting.");
}
n = +n;
if (n < 0) return this.shiftLeft(-n);
var result = this;
while (n >= powers2Length) {
if (result.isZero()) return result;
remQuo = divModAny(result, highestPower2);
result = remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0];
n -= powers2Length - 1;
}
remQuo = divModAny(result, powersOfTwo[n]);
return remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0];
};
SmallInteger.prototype.shiftRight = BigInteger.prototype.shiftRight;
function bitwise(x, y, fn) {
y = parseValue(y);
var xSign = x.isNegative(), ySign = y.isNegative();
var xRem = xSign ? x.not() : x,
yRem = ySign ? y.not() : y;
var xBits = [], yBits = [];
var xStop = false, yStop = false;
while (!xStop || !yStop) {
if (xRem.isZero()) { // virtual sign extension for simulating two's complement
xStop = true;
xBits.push(xSign ? 1 : 0);
}
else if (xSign) xBits.push(xRem.isEven() ? 1 : 0); // two's complement for negative numbers
else xBits.push(xRem.isEven() ? 0 : 1);
if (yRem.isZero()) {
yStop = true;
yBits.push(ySign ? 1 : 0);
}
else if (ySign) yBits.push(yRem.isEven() ? 1 : 0);
else yBits.push(yRem.isEven() ? 0 : 1);
xRem = xRem.over(2);
yRem = yRem.over(2);
}
var result = [];
for (var i = 0; i < xBits.length; i++) result.push(fn(xBits[i], yBits[i]));
var sum = bigInt(result.pop()).negate().times(bigInt(2).pow(result.length));
while (result.length) {
sum = sum.add(bigInt(result.pop()).times(bigInt(2).pow(result.length)));
}
return sum;
}
BigInteger.prototype.not = function () {
return this.negate().prev();
};
SmallInteger.prototype.not = BigInteger.prototype.not;
BigInteger.prototype.and = function (n) {
return bitwise(this, n, function (a, b) { return a & b; });
};
SmallInteger.prototype.and = BigInteger.prototype.and;
BigInteger.prototype.or = function (n) {
return bitwise(this, n, function (a, b) { return a | b; });
};
SmallInteger.prototype.or = BigInteger.prototype.or;
BigInteger.prototype.xor = function (n) {
return bitwise(this, n, function (a, b) { return a ^ b; });
};
SmallInteger.prototype.xor = BigInteger.prototype.xor;
var LOBMASK_I = 1 << 30, LOBMASK_BI = (BASE & -BASE) * (BASE & -BASE) | LOBMASK_I;
function roughLOB(n) { // get lowestOneBit (rough)
// SmallInteger: return Min(lowestOneBit(n), 1 << 30)
// BigInteger: return Min(lowestOneBit(n), 1 << 14) [BASE=1e7]
var v = n.value, x = typeof v === "number" ? v | LOBMASK_I : v[0] + v[1] * BASE | LOBMASK_BI;
return x & -x;
}
function max(a, b) {
a = parseValue(a);
b = parseValue(b);
return a.greater(b) ? a : b;
}
function min(a,b) {
a = parseValue(a);
b = parseValue(b);
return a.lesser(b) ? a : b;
}
function gcd(a, b) {
a = parseValue(a).abs();
b = parseValue(b).abs();
if (a.equals(b)) return a;
if (a.isZero()) return b;
if (b.isZero()) return a;
var c = Integer[1], d, t;
while (a.isEven() && b.isEven()) {
d = Math.min(roughLOB(a), roughLOB(b));
a = a.divide(d);
b = b.divide(d);
c = c.multiply(d);
}
while (a.isEven()) {
a = a.divide(roughLOB(a));
}
do {
while (b.isEven()) {
b = b.divide(roughLOB(b));
}
if (a.greater(b)) {
t = b; b = a; a = t;
}
b = b.subtract(a);
} while (!b.isZero());
return c.isUnit() ? a : a.multiply(c);
}
function lcm(a, b) {
a = parseValue(a).abs();
b = parseValue(b).abs();
return a.divide(gcd(a, b)).multiply(b);
}
function randBetween(a, b) {
a = parseValue(a);
b = parseValue(b);
var low = min(a, b), high = max(a, b);
var range = high.subtract(low);
if (range.isSmall) return low.add(Math.round(Math.random() * range));
var length = range.value.length - 1;
var result = [], restricted = true;
for (var i = length; i >= 0; i--) {
var top = restricted ? range.value[i] : BASE;
var digit = truncate(Math.random() * top);
result.unshift(digit);
if (digit < top) restricted = false;
}
result = arrayToSmall(result);
return low.add(typeof result === "number" ? new SmallInteger(result) : new BigInteger(result, false));
}
var parseBase = function (text, base) {
var val = Integer[0], pow = Integer[1],
length = text.length;
if (2 <= base && base <= 36) {
if (length <= LOG_MAX_INT / Math.log(base)) {
return new SmallInteger(parseInt(text, base));
}
}
base = parseValue(base);
var digits = [];
var i;
var isNegative = text[0] === "-";
for (i = isNegative ? 1 : 0; i < text.length; i++) {
var c = text[i].toLowerCase(),
charCode = c.charCodeAt(0);
if (48 <= charCode && charCode <= 57) digits.push(parseValue(c));
else if (97 <= charCode && charCode <= 122) digits.push(parseValue(c.charCodeAt(0) - 87));
else if (c === "<") {
var start = i;
do { i++; } while (text[i] !== ">");
digits.push(parseValue(text.slice(start + 1, i)));
}
else throw new Error(c + " is not a valid character");
}
digits.reverse();
for (i = 0; i < digits.length; i++) {
val = val.add(digits[i].times(pow));
pow = pow.times(base);
}
return isNegative ? val.negate() : val;
};
function stringify(digit) {
var v = digit.value;
if (typeof v === "number") v = [v];
if (v.length === 1 && v[0] <= 35) {
return "0123456789abcdefghijklmnopqrstuvwxyz".charAt(v[0]);
}
return "<" + v + ">";
}
function toBase(n, base) {
base = bigInt(base);
if (base.isZero()) {
if (n.isZero()) return "0";
throw new Error("Cannot convert nonzero numbers to base 0.");
}
if (base.equals(-1)) {
if (n.isZero()) return "0";
if (n.isNegative()) return new Array(1 - n).join("10");
return "1" + new Array(+n).join("01");
}
var minusSign = "";
if (n.isNegative() && base.isPositive()) {
minusSign = "-";
n = n.abs();
}
if (base.equals(1)) {
if (n.isZero()) return "0";
return minusSign + new Array(+n + 1).join(1);
}
var out = [];
var left = n, divmod;
while (left.isNegative() || left.compareAbs(base) >= 0) {
divmod = left.divmod(base);
left = divmod.quotient;
var digit = divmod.remainder;
if (digit.isNegative()) {
digit = base.minus(digit).abs();
left = left.next();
}
out.push(stringify(digit));
}
out.push(stringify(left));
return minusSign + out.reverse().join("");
}
BigInteger.prototype.toString = function (radix) {
if (radix === undefined) radix = 10;
if (radix !== 10) return toBase(this, radix);
var v = this.value, l = v.length, str = String(v[--l]), zeros = "0000000", digit;
while (--l >= 0) {
digit = String(v[l]);
str += zeros.slice(digit.length) + digit;
}
var sign = this.sign ? "-" : "";
return sign + str;
};
SmallInteger.prototype.toString = function (radix) {
if (radix === undefined) radix = 10;
if (radix != 10) return toBase(this, radix);
return String(this.value);
};
BigInteger.prototype.valueOf = function () {
return +this.toString();
};
BigInteger.prototype.toJSNumber = BigInteger.prototype.valueOf;
SmallInteger.prototype.valueOf = function () {
return this.value;
};
SmallInteger.prototype.toJSNumber = SmallInteger.prototype.valueOf;
function parseStringValue(v) {
if (isPrecise(+v)) {
var x = +v;
if (x === truncate(x))
return new SmallInteger(x);
throw "Invalid integer: " + v;
}
var sign = v[0] === "-";
if (sign) v = v.slice(1);
var split = v.split(/e/i);
if (split.length > 2) throw new Error("Invalid integer: " + split.join("e"));
if (split.length === 2) {
var exp = split[1];
if (exp[0] === "+") exp = exp.slice(1);
exp = +exp;
if (exp !== truncate(exp) || !isPrecise(exp)) throw new Error("Invalid integer: " + exp + " is not a valid exponent.");
var text = split[0];
var decimalPlace = text.indexOf(".");
if (decimalPlace >= 0) {
exp -= text.length - decimalPlace - 1;
text = text.slice(0, decimalPlace) + text.slice(decimalPlace + 1);
}
if (exp < 0) throw new Error("Cannot include negative exponent part for integers");
text += (new Array(exp + 1)).join("0");
v = text;
}
var isValid = /^([0-9][0-9]*)$/.test(v);
if (!isValid) throw new Error("Invalid integer: " + v);
var r = [], max = v.length, l = LOG_BASE, min = max - l;
while (max > 0) {
r.push(+v.slice(min, max));
min -= l;
if (min < 0) min = 0;
max -= l;
}
trim(r);
return new BigInteger(r, sign);
}
function parseNumberValue(v) {
if (isPrecise(v)) {
if (v !== truncate(v)) throw new Error(v + " is not an integer.");
return new SmallInteger(v);
}
return parseStringValue(v.toString());
}
function parseValue(v) {
if (typeof v === "number") {
return parseNumberValue(v);
}
if (typeof v === "string") {
return parseStringValue(v);
}
return v;
}
// Pre-define numbers in range [-999,999]
for (var i = 0; i < 1000; i++) {
Integer[i] = new SmallInteger(i);
if (i > 0) Integer[-i] = new SmallInteger(-i);
}
// Backwards compatibility
Integer.one = Integer[1];
Integer.zero = Integer[0];
Integer.minusOne = Integer[-1];
Integer.max = max;
Integer.min = min;
Integer.gcd = gcd;
Integer.lcm = lcm;
Integer.isInstance = function (x) { return x instanceof BigInteger || x instanceof SmallInteger; };
Integer.randBetween = randBetween;
return Integer;
})();
// Node.js check
if (typeof module !== "undefined" && module.hasOwnProperty("exports")) {
module.exports = bigInt;
}