'use strict';

const bigInt = (function (undefined) {
    "use strict";

    var BASE = 1e7,
      LOG_BASE = 7,
      MAX_INT = 9007199254740992,
      MAX_INT_ARR = smallToArray(MAX_INT),
      DEFAULT_ALPHABET = "0123456789abcdefghijklmnopqrstuvwxyz";

    var supportsNativeBigInt = typeof BigInt === "function";

    function Integer(v, radix, alphabet, caseSensitive) {
        if (typeof v === "undefined") {
            return Integer[0];
        }
        if (typeof radix !== "undefined") {
            return +radix === 10 && !alphabet ? parseValue(v) : parseBase(v, radix, alphabet, caseSensitive);
        }
        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 NativeBigInt(value) {
        this.value = value;
    }

    NativeBigInt.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 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;

    NativeBigInt.prototype.add = function (v) {
        return new NativeBigInt(this.value + parseValue(v).value);
    };
    NativeBigInt.prototype.plus = NativeBigInt.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;
        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;

    NativeBigInt.prototype.subtract = function (v) {
        return new NativeBigInt(this.value - parseValue(v).value);
    };
    NativeBigInt.prototype.minus = NativeBigInt.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;
    };
    NativeBigInt.prototype.negate = function () {
        return new NativeBigInt(-this.value);
    };

    BigInteger.prototype.abs = function () {
        return new BigInteger(this.value, false);
    };
    SmallInteger.prototype.abs = function () {
        return new SmallInteger(Math.abs(this.value));
    };
    NativeBigInt.prototype.abs = function () {
        return new NativeBigInt(this.value >= 0 ? this.value : -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 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;

    NativeBigInt.prototype.multiply = function (v) {
        return new NativeBigInt(this.value * parseValue(v).value);
    };
    NativeBigInt.prototype.times = NativeBigInt.prototype.multiply;

    function square(a) {
        //console.assert(2 * BASE * BASE < MAX_INT);
        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];
            carry = 0 - a_i * a_i;
            for (var j = i; j < l; j++) {
                a_j = a[j];
                product = 2 * (a_i * a_j) + r[i + j] + carry;
                carry = Math.floor(product / base);
                r[i + j] = product - carry * base;
            }
            r[i + l] = 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);
    };

    NativeBigInt.prototype.square = function (v) {
        return new NativeBigInt(this.value * this.value);
    };

    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]);
            trim(part);
            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);
        if (supportsNativeBigInt) {
            return [new NativeBigInt(self.value / n.value), new NativeBigInt(self.value % n.value)];
        }
        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]
        };
    };
    NativeBigInt.prototype.divmod = SmallInteger.prototype.divmod = BigInteger.prototype.divmod;


    BigInteger.prototype.divide = function (v) {
        return divModAny(this, v)[0];
    };
    NativeBigInt.prototype.over = NativeBigInt.prototype.divide = SmallInteger.prototype.over = SmallInteger.prototype.divide
      = BigInteger.prototype.over = BigInteger.prototype.divide;

    BigInteger.prototype.mod = function (v) {
        return divModAny(this, v)[1];
    };
    NativeBigInt.prototype.mod = NativeBigInt.prototype.remainder = 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;

    var pow;
    if (supportsNativeBigInt) {
        // forced to use eval because ** is a syntax error on pre-ECMAScript2017 environments.
        pow = eval("(a,b)=>a**b");
    }

    NativeBigInt.prototype.pow = function (v) {
        var n = parseValue(v);
        var a = this.value, b = n.value;
        if (b === BigInt(0)) {
            return Integer[1];
        }
        if (a === BigInt(0)) {
            return Integer[0];
        }
        if (a === BigInt(1)) {
            return Integer[1];
        }
        if (a === BigInt(-1)) {
            return n.isEven() ? Integer[1] : Integer[-1];
        }
        if (n.isNegative()) {
            return new NativeBigInt(BigInt(0));
        }
        return new NativeBigInt(pow(a, b));
    };

    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;
    };
    NativeBigInt.prototype.modPow = 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;
    };
    NativeBigInt.prototype.compareAbs = function (v) {
        var a = this.value;
        var b = parseValue(v).value;
        a = a >= 0 ? a : -a;
        b = b >= 0 ? b : -b;
        return a === b ? 0 : a > b ? 1 : -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;

    NativeBigInt.prototype.compare = function (v) {
        if (v === Infinity) {
            return -1;
        }
        if (v === -Infinity) {
            return 1;
        }
        var a = this.value;
        var b = parseValue(v).value;
        return a === b ? 0 : a > b ? 1 : -1;
    };
    NativeBigInt.prototype.compareTo = NativeBigInt.prototype.compare;

    BigInteger.prototype.equals = function (v) {
        return this.compare(v) === 0;
    };
    NativeBigInt.prototype.eq = NativeBigInt.prototype.equals = SmallInteger.prototype.eq = SmallInteger.prototype.equals
      = BigInteger.prototype.eq = BigInteger.prototype.equals;

    BigInteger.prototype.notEquals = function (v) {
        return this.compare(v) !== 0;
    };
    NativeBigInt.prototype.neq = NativeBigInt.prototype.notEquals = SmallInteger.prototype.neq = SmallInteger.prototype.notEquals
      = BigInteger.prototype.neq = BigInteger.prototype.notEquals;

    BigInteger.prototype.greater = function (v) {
        return this.compare(v) > 0;
    };
    NativeBigInt.prototype.gt = NativeBigInt.prototype.greater = SmallInteger.prototype.gt = SmallInteger.prototype.greater
      = BigInteger.prototype.gt = BigInteger.prototype.greater;

    BigInteger.prototype.lesser = function (v) {
        return this.compare(v) < 0;
    };
    NativeBigInt.prototype.lt = NativeBigInt.prototype.lesser = SmallInteger.prototype.lt = SmallInteger.prototype.lesser
      = BigInteger.prototype.lt = BigInteger.prototype.lesser;

    BigInteger.prototype.greaterOrEquals = function (v) {
        return this.compare(v) >= 0;
    };
    NativeBigInt.prototype.geq = NativeBigInt.prototype.greaterOrEquals = SmallInteger.prototype.geq
      = SmallInteger.prototype.greaterOrEquals = BigInteger.prototype.geq = BigInteger.prototype.greaterOrEquals;

    BigInteger.prototype.lesserOrEquals = function (v) {
        return this.compare(v) <= 0;
    };
    NativeBigInt.prototype.leq = NativeBigInt.prototype.lesserOrEquals = 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;
    };
    NativeBigInt.prototype.isEven = function () {
        return (this.value & BigInt(1)) === BigInt(0);
    };

    BigInteger.prototype.isOdd = function () {
        return (this.value[0] & 1) === 1;
    };
    SmallInteger.prototype.isOdd = function () {
        return (this.value & 1) === 1;
    };
    NativeBigInt.prototype.isOdd = function () {
        return (this.value & BigInt(1)) === BigInt(1);
    };

    BigInteger.prototype.isPositive = function () {
        return !this.sign;
    };
    SmallInteger.prototype.isPositive = function () {
        return this.value > 0;
    };
    NativeBigInt.prototype.isPositive = SmallInteger.prototype.isPositive;

    BigInteger.prototype.isNegative = function () {
        return this.sign;
    };
    SmallInteger.prototype.isNegative = function () {
        return this.value < 0;
    };
    NativeBigInt.prototype.isNegative = SmallInteger.prototype.isNegative;

    BigInteger.prototype.isUnit = function () {
        return false;
    };
    SmallInteger.prototype.isUnit = function () {
        return Math.abs(this.value) === 1;
    };
    NativeBigInt.prototype.isUnit = function () {
        return this.abs().value === BigInt(1);
    };

    BigInteger.prototype.isZero = function () {
        return false;
    };
    SmallInteger.prototype.isZero = function () {
        return this.value === 0;
    };
    NativeBigInt.prototype.isZero = function () {
        return this.value === BigInt(0);
    };

    BigInteger.prototype.isDivisibleBy = function (v) {
        var n = parseValue(v);
        if (n.isZero()) {
            return false;
        }
        if (n.isUnit()) {
            return true;
        }
        if (n.compareAbs(2) === 0) {
            return this.isEven();
        }
        return this.mod(n).isZero();
    };
    NativeBigInt.prototype.isDivisibleBy = 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(49)) {
            return true;
        }
        // we don't know if it's prime: let the other functions figure it out
    }

    function millerRabinTest(n, a) {
        var nPrev = n.prev(),
          b = nPrev,
          r = 0,
          d, t, i, x;
        while (b.isEven()) {
            b = b.divide(2), r++;
        }
        next: for (i = 0; i < a.length; i++) {
            if (n.lesser(a[i])) {
                continue;
            }
            x = bigInt(a[i]).modPow(b, n);
            if (x.isUnit() || x.equals(nPrev)) {
                continue;
            }
            for (d = r - 1; d != 0; d--) {
                x = x.square().mod(n);
                if (x.isUnit()) {
                    return false;
                }
                if (x.equals(nPrev)) {
                    continue next;
                }
            }
            return false;
        }
        return true;
    }

    // Set "strict" to true to force GRH-supported lower bound of 2*log(N)^2
    BigInteger.prototype.isPrime = function (strict) {
        var isPrime = isBasicPrime(this);
        if (isPrime !== undefined) {
            return isPrime;
        }
        var n = this.abs();
        var bits = n.bitLength();
        if (bits <= 64) {
            return millerRabinTest(n, [2, 325, 9375, 28178, 450775, 9780504, 1795265022]);
        }
        var logN = Math.log(2) * bits.toJSNumber();
        var t = Math.ceil((strict === true) ? (2 * Math.pow(logN, 2)) : logN);
        for (var a = [], i = 0; i < t; i++) {
            a.push(bigInt(i + 2));
        }
        return millerRabinTest(n, a);
    };
    NativeBigInt.prototype.isPrime = 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;
        for (var a = [], i = 0; i < t; i++) {
            a.push(bigInt.randBetween(2, n.minus(2)));
        }
        return millerRabinTest(n, a);
    };
    NativeBigInt.prototype.isProbablePrime = SmallInteger.prototype.isProbablePrime = BigInteger.prototype.isProbablePrime;

    BigInteger.prototype.modInv = function (n) {
        var t = bigInt.zero, newT = bigInt.one, r = parseValue(n), newR = this.abs(), q, lastT, lastR;
        while (!newR.isZero()) {
            q = r.divide(newR);
            lastT = t;
            lastR = r;
            t = newT;
            r = newR;
            newT = lastT.subtract(q.multiply(newT));
            newR = lastR.subtract(q.multiply(newR));
        }
        if (!r.isUnit()) {
            throw new Error(this.toString() + " and " + n.toString() + " are not co-prime");
        }
        if (t.compare(0) === -1) {
            t = t.add(n);
        }
        if (this.isNegative()) {
            return t.negate();
        }
        return t;
    };

    NativeBigInt.prototype.modInv = SmallInteger.prototype.modInv = BigInteger.prototype.modInv;

    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);
    };
    NativeBigInt.prototype.next = function () {
        return new NativeBigInt(this.value + BigInt(1));
    };

    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);
    };
    NativeBigInt.prototype.prev = function () {
        return new NativeBigInt(this.value - BigInt(1));
    };

    var powersOfTwo = [1];
    while (2 * 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 Math.abs(n) <= BASE;
    }

    BigInteger.prototype.shiftLeft = function (v) {
        var n = parseValue(v).toJSNumber();
        if (!shift_isSmall(n)) {
            throw new Error(String(n) + " is too large for shifting.");
        }
        if (n < 0) {
            return this.shiftRight(-n);
        }
        var result = this;
        if (result.isZero()) {
            return result;
        }
        while (n >= powers2Length) {
            result = result.multiply(highestPower2);
            n -= powers2Length - 1;
        }
        return result.multiply(powersOfTwo[n]);
    };
    NativeBigInt.prototype.shiftLeft = SmallInteger.prototype.shiftLeft = BigInteger.prototype.shiftLeft;

    BigInteger.prototype.shiftRight = function (v) {
        var remQuo;
        var n = parseValue(v).toJSNumber();
        if (!shift_isSmall(n)) {
            throw new Error(String(n) + " is too large for shifting.");
        }
        if (n < 0) {
            return this.shiftLeft(-n);
        }
        var result = this;
        while (n >= powers2Length) {
            if (result.isZero() || (result.isNegative() && result.isUnit())) {
                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];
    };
    NativeBigInt.prototype.shiftRight = 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 xDigit = 0, yDigit = 0;
        var xDivMod = null, yDivMod = null;
        var result = [];
        while (!xRem.isZero() || !yRem.isZero()) {
            xDivMod = divModAny(xRem, highestPower2);
            xDigit = xDivMod[1].toJSNumber();
            if (xSign) {
                xDigit = highestPower2 - 1 - xDigit; // two's complement for negative numbers
            }

            yDivMod = divModAny(yRem, highestPower2);
            yDigit = yDivMod[1].toJSNumber();
            if (ySign) {
                yDigit = highestPower2 - 1 - yDigit; // two's complement for negative numbers
            }

            xRem = xDivMod[0];
            yRem = yDivMod[0];
            result.push(fn(xDigit, yDigit));
        }
        var sum = fn(xSign ? 1 : 0, ySign ? 1 : 0) !== 0 ? bigInt(-1) : bigInt(0);
        for (var i = result.length - 1; i >= 0; i -= 1) {
            sum = sum.multiply(highestPower2).add(bigInt(result[i]));
        }
        return sum;
    }

    BigInteger.prototype.not = function () {
        return this.negate().prev();
    };
    NativeBigInt.prototype.not = SmallInteger.prototype.not = BigInteger.prototype.not;

    BigInteger.prototype.and = function (n) {
        return bitwise(this, n, function (a, b) {
            return a & b;
        });
    };
    NativeBigInt.prototype.and = SmallInteger.prototype.and = BigInteger.prototype.and;

    BigInteger.prototype.or = function (n) {
        return bitwise(this, n, function (a, b) {
            return a | b;
        });
    };
    NativeBigInt.prototype.or = SmallInteger.prototype.or = BigInteger.prototype.or;

    BigInteger.prototype.xor = function (n) {
        return bitwise(this, n, function (a, b) {
            return a ^ b;
        });
    };
    NativeBigInt.prototype.xor = 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 :
              typeof v === "bigint" ? v | BigInt(LOBMASK_I) :
              v[0] + v[1] * BASE | LOBMASK_BI;
        return x & -x;
    }

    function integerLogarithm(value, base) {
        if (base.compareTo(value) <= 0) {
            var tmp = integerLogarithm(value, base.square(base));
            var p = tmp.p;
            var e = tmp.e;
            var t = p.multiply(base);
            return t.compareTo(value) <= 0 ? {p: t, e: e * 2 + 1} : {p: p, e: e * 2};
        }
        return {p: bigInt(1), e: 0};
    }

    BigInteger.prototype.bitLength = function () {
        var n = this;
        if (n.compareTo(bigInt(0)) < 0) {
            n = n.negate().subtract(bigInt(1));
        }
        if (n.compareTo(bigInt(0)) === 0) {
            return bigInt(0);
        }
        return bigInt(integerLogarithm(n, bigInt(2)).e).add(bigInt(1));
    };
    NativeBigInt.prototype.bitLength = SmallInteger.prototype.bitLength = BigInteger.prototype.bitLength;

    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 = 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).add(1);
        if (range.isSmall) {
            return low.add(Math.floor(Math.random() * range));
        }
        var digits = toBase(range, BASE).value;
        var result = [], restricted = true;
        for (var i = 0; i < digits.length; i++) {
            var top = restricted ? digits[i] : BASE;
            var digit = truncate(Math.random() * top);
            result.push(digit);
            if (digit < top) {
                restricted = false;
            }
        }
        return low.add(Integer.fromArray(result, BASE, false));
    }

    var parseBase = function (text, base, alphabet, caseSensitive) {
        alphabet = alphabet || DEFAULT_ALPHABET;
        text = String(text);
        if (!caseSensitive) {
            text = text.toLowerCase();
            alphabet = alphabet.toLowerCase();
        }
        var length = text.length;
        var i;
        var absBase = Math.abs(base);
        var alphabetValues = {};
        for (i = 0; i < alphabet.length; i++) {
            alphabetValues[alphabet[i]] = i;
        }
        for (i = 0; i < length; i++) {
            var c = text[i];
            if (c === "-") {
                continue;
            }
            if (c in alphabetValues) {
                if (alphabetValues[c] >= absBase) {
                    if (c === "1" && absBase === 1) {
                        continue;
                    }
                    throw new Error(c + " is not a valid digit in base " + base + ".");
                }
            }
        }
        base = parseValue(base);
        var digits = [];
        var isNegative = text[0] === "-";
        for (i = isNegative ? 1 : 0; i < text.length; i++) {
            var c = text[i];
            if (c in alphabetValues) {
                digits.push(parseValue(alphabetValues[c]));
            } else if (c === "<") {
                var start = i;
                do {
                    i++;
                } while (text[i] !== ">" && i < text.length);
                digits.push(parseValue(text.slice(start + 1, i)));
            } else {
                throw new Error(c + " is not a valid character");
            }
        }
        return parseBaseFromArray(digits, base, isNegative);
    };

    function parseBaseFromArray(digits, base, isNegative) {
        var val = Integer[0], pow = Integer[1], i;
        for (i = digits.length - 1; i >= 0; i--) {
            val = val.add(digits[i].times(pow));
            pow = pow.times(base);
        }
        return isNegative ? val.negate() : val;
    }

    function stringify(digit, alphabet) {
        alphabet = alphabet || DEFAULT_ALPHABET;
        if (digit < alphabet.length) {
            return alphabet[digit];
        }
        return "<" + digit + ">";
    }

    function toBase(n, base) {
        base = bigInt(base);
        if (base.isZero()) {
            if (n.isZero()) {
                return {value: [0], isNegative: false};
            }
            throw new Error("Cannot convert nonzero numbers to base 0.");
        }
        if (base.equals(-1)) {
            if (n.isZero()) {
                return {value: [0], isNegative: false};
            }
            if (n.isNegative()) {
                return {
                    value: [].concat.apply([], Array.apply(null, Array(-n.toJSNumber()))
                      .map(Array.prototype.valueOf, [1, 0])
                    ),
                    isNegative: false
                };
            }

            var arr = Array.apply(null, Array(n.toJSNumber() - 1))
              .map(Array.prototype.valueOf, [0, 1]);
            arr.unshift([1]);
            return {
                value: [].concat.apply([], arr),
                isNegative: false
            };
        }

        var neg = false;
        if (n.isNegative() && base.isPositive()) {
            neg = true;
            n = n.abs();
        }
        if (base.isUnit()) {
            if (n.isZero()) {
                return {value: [0], isNegative: false};
            }

            return {
                value: Array.apply(null, Array(n.toJSNumber()))
                  .map(Number.prototype.valueOf, 1),
                isNegative: neg
            };
        }
        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(digit.toJSNumber());
        }
        out.push(left.toJSNumber());
        return {value: out.reverse(), isNegative: neg};
    }

    function toBaseString(n, base, alphabet) {
        var arr = toBase(n, base);
        return (arr.isNegative ? "-" : "") + arr.value.map(function (x) {
            return stringify(x, alphabet);
        }).join('');
    }

    BigInteger.prototype.toArray = function (radix) {
        return toBase(this, radix);
    };

    SmallInteger.prototype.toArray = function (radix) {
        return toBase(this, radix);
    };

    NativeBigInt.prototype.toArray = function (radix) {
        return toBase(this, radix);
    };

    BigInteger.prototype.toString = function (radix, alphabet) {
        if (radix === undefined) {
            radix = 10;
        }
        if (radix !== 10) {
            return toBaseString(this, radix, alphabet);
        }
        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, alphabet) {
        if (radix === undefined) {
            radix = 10;
        }
        if (radix != 10) {
            return toBaseString(this, radix, alphabet);
        }
        return String(this.value);
    };

    NativeBigInt.prototype.toString = SmallInteger.prototype.toString;

    NativeBigInt.prototype.toJSON = BigInteger.prototype.toJSON = SmallInteger.prototype.toJSON = function () {
        return this.toString();
    };

    BigInteger.prototype.valueOf = function () {
        return parseInt(this.toString(), 10);
    };
    BigInteger.prototype.toJSNumber = BigInteger.prototype.valueOf;

    SmallInteger.prototype.valueOf = function () {
        return this.value;
    };
    SmallInteger.prototype.toJSNumber = SmallInteger.prototype.valueOf;
    NativeBigInt.prototype.valueOf = NativeBigInt.prototype.toJSNumber = function () {
        return parseInt(this.toString(), 10);
    };

    function parseStringValue(v) {
        if (isPrecise(+v)) {
            var x = +v;
            if (x === truncate(x)) {
                return supportsNativeBigInt ? new NativeBigInt(BigInt(x)) : new SmallInteger(x);
            }
            throw new Error("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);
        }
        if (supportsNativeBigInt) {
            return new NativeBigInt(BigInt(sign ? "-" + v : 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 (supportsNativeBigInt) {
            return new NativeBigInt(BigInt(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);
        }
        if (typeof v === "bigint") {
            return new NativeBigInt(v);
        }
        return v;
    }

    // Pre-define numbers in range [-999,999]
    for (var i = 0; i < 1000; i++) {
        Integer[i] = parseValue(i);
        if (i > 0) {
            Integer[-i] = parseValue(-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 || x instanceof NativeBigInt;
    };
    Integer.randBetween = randBetween;

    Integer.fromArray = function (digits, base, isNegative) {
        return parseBaseFromArray(digits.map(parseValue), parseValue(base || 10), isNegative);
    };

    return Integer;
})();

new Promise(function (resolve) {
    const lines = [];
    const reader = require('readline').createInterface({input: process.stdin, output: process.stdout});
    reader.on('line', function (line) {
        lines.push(line.split(' '));
    });
    reader.on('close', function () {
        resolve(lines);
    });
}).then(function (lines) {
    const l = bigInt(lines[0][0]);
    const r = bigInt(lines[0][1]);
    console.log(search(l, r, bigInt(2019)));
});

function search(lower, upper, mod) {
    let min_remain = mod;
    let i = lower;
    while (i.lesserOrEquals(bigInt.min(lower.add(mod).minus(lower.mod(mod)), upper.minus(bigInt.one)))) {
        let j = i.add(bigInt.one);
        while (j.lesserOrEquals(bigInt.min(i.add(mod), upper))) {
            const remain = i.multiply(j).mod(mod);
            if (remain.isZero()) {
                return 0;
            }
            if (min_remain.greater(remain)) {
                min_remain = remain;
            }
            j = j.add(bigInt.one);
        }
        i = i.add(bigInt.one);
    }
    return min_remain.toString();
}



Measured memory_bytes: 15392