struct BigInteger {
    typedef unsigned long long LL;
 
    static const int BASE = 100000000;
    static const int WIDTH = 8;
    vector<int> s;
 
    BigInteger& clean() { while (!s.back() && s.size() > 1)s.pop_back(); return *this; }
    BigInteger(LL num = 0) { *this = num; }
    BigInteger(
 
string s) { *this = s; }
    BigInteger& operator = (long long num) {
        s.clear();
        do {
            s.push_back(num % BASE);
            num /= BASE;
        } while (num > 0);
        return *this;
    }
    BigInteger& operator = (const string& str) {
        s.clear();
        
 
int x, len = (str.length() - 1) / WIDTH + 1;
        for (int i = 0; i < len; i++) {
            int end = str.length() - i * WIDTH;
            int start = max(0, end - WIDTH);
            sscanf(str.substr(start, end - start).c_str(), "%d", &x);
            s.push_back(x);
        }
        return
 
 (*this).clean();
    }
 
    BigInteger operator + (const BigInteger& b) const {
        BigInteger c; c.s.clear();
        for (int i = 0, g = 0; ; i++) {
            if (g == 0 && i >= s.size() && i >= b.s.size()) break;
            int x = g;
            if (i < s.size()) x += s[i];
            if (i < b.s.size()) x += b.s[i];
            c.s.push_back(x % BASE);
            g = x / BASE;
        }
        return c;
    }
    BigInteger operator - (const BigInteger& b) const {
        assert(b <= *this); // 減數不能大於被減數
        BigInteger c; c.s.clear();
        for (int i = 0, g = 0; ; i++) {
            if (g == 0 && i >= s.size() && i >= b.s.size()) break;
            int x = s[i] + g;
            if (i < b.s.size()) x -= b.s[i];
            if (x < 0) { g = -1; x += BASE; }
            else g = 0;
            c.s.push_back(x);
        }
        return c.clean();
    }
    BigInteger operator * (const BigInteger& b) const {
        int i, j; LL g;
        vector<LL> v(s.size() + b.s.size(), 0);
        BigInteger c; c.s.clear();
        for (i = 0; i < s.size(); i++) for (j = 0; j < b.s.size(); j++) v[i + j] += LL(s[i]) * b.s[j];
        for (i = 0, g = 0; ; i++) {
            if (g == 0 && i >= v.size()) break;
            LL x = v[i] + g;
            c.s.push_back(x % BASE);
            g = x / BASE;
        }
        return c.clean();
    }
    BigInteger operator / (const BigInteger& b) const {
        assert(b > 0);  // 除數必須大於0
        BigInteger c = *this;       // 商:主要是讓c.s和(*this).s的vector一樣大
        BigInteger m;               // 餘數:初始化為0
        for (int i = s.size() - 1; i >= 0; i--) {
            m = m * BASE + s[i];
            c.s[i] = bsearch(b, m);
            m -= b * c.s[i];
        }
        return c.clean();
    }
    BigInteger operator % (const BigInteger& b) const { //方法與除法相同
        BigInteger c = *this;
        BigInteger m;
        for (int i = s.size() - 1; i >= 0; i--) {
            m = m * BASE + s[i];
            c.s[i] = bsearch(b, m);
            m -= b * c.s[i];
        }
        return m;
    }
    // 二分法找出滿足bx<=m的最大的x
    int bsearch(const BigInteger& b, const BigInteger& m) const {
        int L = 0, R = BASE - 1, x;
        while (1) {
            x = (L + R) >> 1;
            if (b * x <= m) { if (b * (x + 1) > m) return x; else L = x; }
            else R = x;
        }
    }
    BigInteger& operator += (const BigInteger& b) { *this = *this + b; return *this; }
    BigInteger& operator -= (const BigInteger& b) { *this = *this - b; return *this; }
    BigInteger& operator *= (const BigInteger& b) { *this = *this * b; return *this; }
    BigInteger& operator /= (const BigInteger& b) { *this = *this / b; return *this; }
    BigInteger& operator %= (const BigInteger& b) { *this = *this % b; return *this; }
 
    bool operator < (const BigInteger& b) const {
        if (s.size() != b.s.size()) return s.size() < b.s.size();
        for (int i = s.size() - 1; i >= 0; i--)
            if (s[i] != b.s[i]) return s[i] < b.s[i];
        return false;
    }
    bool operator >(const BigInteger& b) const { return b < *this; }
    bool operator<=(const BigInteger& b) const { return !(b < *this); }
    bool operator>=(const BigInteger& b) const { return !(*this < b); }
    bool operator!=(const BigInteger& b) const { return b < *this || *this < b; }
    bool operator==(const BigInteger& b) const { return !(b < *this) && !(b > * this); }
};
 
ostream& operator << (ostream& out, const BigInteger& x) {
    out << x.s.back();
    for (int i = x.s.size() - 2; i >= 0; i--) {
        char buf[20];
        sprintf(buf, "%08d", x.s[i]);
        for (int j = 0; j < strlen(buf); j++) out << buf[j];
    }
    return out;
}
 
istream& operator >> (istream& in, BigInteger& x) {
    string s;
    if (!(in >> s)) return in;
    x = s;
    return in;
}
 
 
BigInteger gcd(BigInteger m, BigInteger n)
{
    return n == 0 ? m : gcd(n, m % n);
}
 
BigInteger lcm(BigInteger m, BigInteger n)
{
    return n * m / gcd(m, n);
}