高精度(Arbitrary-precision arithmetic)

#include <bits/stdc++.h>
using namespace std;

struct BigInteger {
    static const int BASE = 100000000;
    static const int WIDTH = 8;
    vector<int> s;

    BigInteger(long long num = 0) { *this = num; }
    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;
    }
    friend 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;
    }
    friend istream& operator >> (istream &in, BigInteger& x){
        string st;
        if(!(in >> st)) return in;
        x = st;
        return in;
    }
    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){
        *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) && !(*this < b); }

};
int main() {
    BigInteger a, b;
    cin >> a >> b;
    cout << "a= " << a << endl << "b= " << b << endl;
    cout << "a+b= " << (a+b) << endl;
    cout << "a<b " << (a<b) << endl;
    cout << "a>b " << (a>b) << endl;
    cout << "a<=b " << (a<=b) << endl;
    cout << "a>=b " << (a>=b) << endl;
    cout << "a!=b " << (a!=b) << endl;
    cout << "a==b " << (a==b) << endl;
    return 0;
}

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <string>
#include <algorithm>

using namespace std;

const int MAXN = 410;

struct BigInteger {
    int len, s[MAXN];

    BigInteger() {
        memset(s, 0, sizeof(s));
        len = 1;
    }

    BigInteger(int num) { *this = num; }

    BigInteger(const char *num) { *this = num; }

    BigInteger operator=(const int num) {
        char s[MAXN];
        sprintf(s, "%d", num);
        *this = s;
        return *this;
    }

    BigInteger operator=(const char *num) {
        for (int i = 0; num[i] == '0'; num++);  //去前导0
        len = strlen(num);
        for (int i = 0; i < len; i++) s[i] = num[len - i - 1] - '0';
        return *this;
    }

    BigInteger operator+(const BigInteger &b) const //+
    {
        BigInteger c;
        c.len = 0;
        for (int i = 0, g = 0; g || i < max(len, b.len); i++) {
            int x = g;
            if (i < len) x += s[i];
            if (i < b.len) x += b.s[i];
            c.s[c.len++] = x % 10;
            g = x / 10;
        }
        return c;
    }

    BigInteger operator+=(const BigInteger &b) {
        *this = *this + b;
        return *this;
    }

    void clean() {
        while (len > 1 && !s[len - 1]) len--;
    }

    BigInteger operator*(const BigInteger &b) //*
    {
        BigInteger c;
        c.len = len + b.len;
        for (int i = 0; i < len; i++) {
            for (int j = 0; j < b.len; j++) {
                c.s[i + j] += s[i] * b.s[j];
            }
        }
        for (int i = 0; i < c.len; i++) {
            c.s[i + 1] += c.s[i] / 10;
            c.s[i] %= 10;
        }
        c.clean();
        return c;
    }

    BigInteger operator*=(const BigInteger &b) {
        *this = *this * b;
        return *this;
    }

    BigInteger operator-(const BigInteger &b) {
        BigInteger c;
        c.len = 0;
        for (int i = 0, g = 0; i < len; i++) {
            int x = s[i] - g;
            if (i < b.len) x -= b.s[i];
            if (x >= 0) g = 0;
            else {
                g = 1;
                x += 10;
            }
            c.s[c.len++] = x;
        }
        c.clean();
        return c;
    }

    BigInteger operator-=(const BigInteger &b) {
        *this = *this - b;
        return *this;
    }

    BigInteger operator/(const BigInteger &b) {
        BigInteger c, f = 0;
        for (int i = len - 1; i >= 0; i--) {
            f = f * 10;
            f.s[0] = s[i];
            while (f >= b) {
                f -= b;
                c.s[i]++;
            }
        }
        c.len = len;
        c.clean();
        return c;
    }

    BigInteger operator/=(const BigInteger &b) {
        *this = *this / b;
        return *this;
    }

    BigInteger operator%(const BigInteger &b) {
        BigInteger r = *this / b;
        r = *this - r * b;
        return r;
    }

    BigInteger operator%=(const BigInteger &b) {
        *this = *this % b;
        return *this;
    }

    bool operator<(const BigInteger &b) {
        if (len != b.len) return len < b.len;
        for (int i = len - 1; i >= 0; i--) {
            if (s[i] != b.s[i]) return s[i] < b.s[i];
        }
        return false;
    }

    bool operator>(const BigInteger &b) {
        if (len != b.len) return len > b.len;
        for (int i = len - 1; i >= 0; i--) {
            if (s[i] != b.s[i]) return s[i] > b.s[i];
        }
        return false;
    }

    bool operator==(const BigInteger &b) {
        return !(*this > b) && !(*this < b);
    }

    bool operator!=(const BigInteger &b) {
        return !(*this == b);
    }

    bool operator<=(const BigInteger &b) {
        return *this < b || *this == b;
    }

    bool operator>=(const BigInteger &b) {
        return *this > b || *this == b;
    }

    string str() const {
        string res = "";
        for (int i = 0; i < len; i++) res = char(s[i] + '0') + res;
        return res;
    }
};

istream &operator>>(istream &in, BigInteger &x) {
    string s;
    in >> s;
    x = s.c_str();
    return in;
}

ostream &operator<<(ostream &out, const BigInteger &x) {
    out << x.str();
    return out;
}

int main() {
    BigInteger a, b, c, d, e, f, g;
    while (cin >> a >> b) {
        a.clean(), b.clean();
        c = a + b;
        d = a - b;
        e = a * b;
        f = a / b;
        g = a % b;
        cout << "a+b" << "=" << c << endl; // a += b
        cout << "a-b" << "=" << d << endl; // a -= b;
        cout << "a*b" << "=" << e << endl; // a *= b;
        cout << "a/b" << "=" << f << endl; // a /= b;
        cout << "a%b" << "=" << g << endl; // a %= b;
        if (a != b) printf("YES\n");
        else printf("NO\n");
    }
    return 0;
} 

#include <bits/stdc++.h>
using namespace std;
// base and base_digits must be consistent
constexpr int base = 1000000000;
constexpr int base_digits = 9;

struct bigint {
    // value == 0 is represented by empty z
    vector<int> z; // digits

    // sign == 1 <==> value >= 0
    // sign == -1 <==> value < 0
    int sign;

    bigint() : sign(1) {}
    bigint(long long v) { *this = v; }

    bigint &operator=(long long v) {
        sign = v < 0 ? -1 : 1; v *= sign;
        z.clear(); for (; v > 0; v = v / base) z.push_back((int) (v % base));
        return *this;
    }

    bigint(const string &s) { read(s); }

    bigint &operator+=(const bigint &other) {
        if (sign == other.sign) {
            for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
                if (i == z.size())
                    z.push_back(0);
                z[i] += carry + (i < other.z.size() ? other.z[i] : 0);
                carry = z[i] >= base;
                if (carry)
                    z[i] -= base;
            }
        } else if (other != 0 /* prevent infinite loop */) {
            *this -= -other;
        }
        return *this;
    }

    friend bigint operator+(bigint a, const bigint &b) { return a += b; }

    bigint &operator-=(const bigint &other) {
        if (sign == other.sign) {
            if (sign == 1 && *this >= other || sign == -1 && *this <= other) {
                for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
                    z[i] -= carry + (i < other.z.size() ? other.z[i] : 0);
                    carry = z[i] < 0;
                    if (carry)
                        z[i] += base;
                }
                trim();
            } else {
                *this = other - *this;
                this->sign = -this->sign;
            }
        } else {
            *this += -other;
        }
        return *this;
    }

    friend bigint operator-(bigint a, const bigint &b) { return a -= b; }

    bigint &operator*=(int v) {
        if (v < 0) sign = -sign, v = -v;
        for (int i = 0, carry = 0; i < z.size() || carry; ++i) {
            if (i == z.size())
                z.push_back(0);
            long long cur = (long long) z[i] * v + carry;
            carry = (int) (cur / base);
            z[i] = (int) (cur % base);
        }
        trim();
        return *this;
    }

    bigint operator*(int v) const { return bigint(*this) *= v; }

    friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
        int norm = base / (b1.z.back() + 1);
        bigint a = a1.abs() * norm;
        bigint b = b1.abs() * norm;
        bigint q, r;
        q.z.resize(a.z.size());

        for (int i = (int) a.z.size() - 1; i >= 0; i--) {
            r *= base;
            r += a.z[i];
            int s1 = b.z.size() < r.z.size() ? r.z[b.z.size()] : 0;
            int s2 = b.z.size() - 1 < r.z.size() ? r.z[b.z.size() - 1] : 0;
            int d = (int) (((long long) s1 * base + s2) / b.z.back());
            r -= b * d;
            while (r < 0)
                r += b, --d;
            q.z[i] = d;
        }

        q.sign = a1.sign * b1.sign;
        r.sign = a1.sign;
        q.trim();
        r.trim();
        return {q, r / norm};
    }

    friend bigint sqrt(const bigint &a1) {
        bigint a = a1;
        while (a.z.empty() || a.z.size() % 2 == 1)
            a.z.push_back(0);

        int n = a.z.size();

        int firstDigit = (int) ::sqrt((double) a.z[n - 1] * base + a.z[n - 2]);
        int norm = base / (firstDigit + 1);
        a *= norm;
        a *= norm;
        while (a.z.empty() || a.z.size() % 2 == 1)
            a.z.push_back(0);

        bigint r = (long long) a.z[n - 1] * base + a.z[n - 2];
        firstDigit = (int) ::sqrt((double) a.z[n - 1] * base + a.z[n - 2]);
        int q = firstDigit;
        bigint res;

        for (int j = n / 2 - 1; j >= 0; j--) {
            for (;; --q) {
                bigint r1 = (r - (res * 2 * base + q) * q) * base * base +
                            (j > 0 ? (long long) a.z[2 * j - 1] * base + a.z[2 * j - 2] : 0);
                if (r1 >= 0) {
                    r = r1;
                    break;
                }
            }
            res *= base;
            res += q;

            if (j > 0) {
                int d1 = res.z.size() + 2 < r.z.size() ? r.z[res.z.size() + 2] : 0;
                int d2 = res.z.size() + 1 < r.z.size() ? r.z[res.z.size() + 1] : 0;
                int d3 = res.z.size() < r.z.size() ? r.z[res.z.size()] : 0;
                q = (int) (((long long) d1 * base * base + (long long) d2 * base + d3) / (firstDigit * 2));
            }
        }

        res.trim();
        return res / norm;
    }

    bigint operator/(const bigint &v) const { return divmod(*this, v).first; }

    bigint operator%(const bigint &v) const { return divmod(*this, v).second; }

    bigint &operator/=(int v) {
        if (v < 0) sign = -sign, v = -v;
        for (int i = (int) z.size() - 1, rem = 0; i >= 0; --i) {
            long long cur = z[i] + rem * (long long) base;
            z[i] = (int) (cur / v);
            rem = (int) (cur % v);
        }
        trim();
        return *this;
    }

    bigint operator/(int v) const { return bigint(*this) /= v; }

    int operator%(int v) const {
        if (v < 0) v = -v;
        int m = 0;
        for (int i = (int) z.size() - 1; i >= 0; --i)
            m = (int) ((z[i] + m * (long long) base) % v);
        return m * sign;
    }

    bigint &operator*=(const bigint &v) { return *this = *this * v; }
    bigint &operator/=(const bigint &v) { return *this = *this / v; }

    bool operator<(const bigint &v) const {
        if (sign != v.sign)
            return sign < v.sign;
        if (z.size() != v.z.size())
            return z.size() * sign < v.z.size() * v.sign;
        for (int i = (int) z.size() - 1; i >= 0; i--)
            if (z[i] != v.z[i])
                return z[i] * sign < v.z[i] * sign;
        return false;
    }

    bool operator>(const bigint &v) const { return v < *this; }
    bool operator<=(const bigint &v) const { return !(v < *this); }
    bool operator>=(const bigint &v) const { return !(*this < v); }

    bool operator==(const bigint &v) const { return !(*this < v) && !(v < *this); }

    bool operator!=(const bigint &v) const { return *this < v || v < *this; }

    void trim() {
        while (!z.empty() && z.back() == 0) z.pop_back();
        if (z.empty()) sign = 1;
    }

    bool isZero() const { return z.empty(); }

    friend bigint operator-(bigint v) {
        if (!v.z.empty()) v.sign = -v.sign;
        return v;
    }

    bigint abs() const {
        return sign == 1 ? *this : -*this;
    }

    long long longValue() const {
        long long res = 0;
        for (int i = (int) z.size() - 1; i >= 0; i--)
            res = res * base + z[i];
        return res * sign;
    }

    friend bigint gcd(const bigint &a, const bigint &b) {
        return b.isZero() ? a : gcd(b, a % b);
    }

    friend bigint lcm(const bigint &a, const bigint &b) {
        return a / gcd(a, b) * b;
    }

    void read(const string &s) {
        sign = 1;
        z.clear();
        int pos = 0;
        while (pos < s.size() && (s[pos] == '-' || s[pos] == '+')) {
            if (s[pos] == '-')
                sign = -sign;
            ++pos;
        }
        for (int i = (int) s.size() - 1; i >= pos; i -= base_digits) {
            int x = 0;
            for (int j = max(pos, i - base_digits + 1); j <= i; j++)
                x = x * 10 + s[j] - '0';
            z.push_back(x);
        }
        trim();
    }

    friend istream &operator>>(istream &stream, bigint &v) {
        string s; stream >> s;
        v.read(s);
        return stream;
    }

    friend ostream &operator<<(ostream &stream, const bigint &v) {
        if (v.sign == -1)
            stream << '-';
        stream << (v.z.empty() ? 0 : v.z.back());
        for (int i = (int) v.z.size() - 2; i >= 0; --i)
            stream << setw(base_digits) << setfill('0') << v.z[i];
        return stream;
    }

    static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
        vector<long long> p(max(old_digits, new_digits) + 1);
        p[0] = 1;
        for (int i = 1; i < p.size(); i++)
            p[i] = p[i - 1] * 10;
        vector<int> res;
        long long cur = 0;
        int cur_digits = 0;
        for (int v : a) {
            cur += v * p[cur_digits];
            cur_digits += old_digits;
            while (cur_digits >= new_digits) {
                res.push_back(int(cur % p[new_digits]));
                cur /= p[new_digits];
                cur_digits -= new_digits;
            }
        }
        res.push_back((int) cur);
        while (!res.empty() && res.back() == 0)
            res.pop_back();
        return res;
    }

    typedef vector<long long> vll;

    static vll karatsubaMultiply(const vll &a, const vll &b) {
        int n = a.size();
        vll res(n + n);
        if (n <= 32) {
            for (int i = 0; i < n; i++)
                for (int j = 0; j < n; j++)
                    res[i + j] += a[i] * b[j];
            return res;
        }

        int k = n >> 1;
        vll a1(a.begin(), a.begin() + k);
        vll a2(a.begin() + k, a.end());
        vll b1(b.begin(), b.begin() + k);
        vll b2(b.begin() + k, b.end());

        vll a1b1 = karatsubaMultiply(a1, b1);
        vll a2b2 = karatsubaMultiply(a2, b2);

        for (int i = 0; i < k; i++)
            a2[i] += a1[i];
        for (int i = 0; i < k; i++)
            b2[i] += b1[i];

        vll r = karatsubaMultiply(a2, b2);
        for (int i = 0; i < a1b1.size(); i++)
            r[i] -= a1b1[i];
        for (int i = 0; i < a2b2.size(); i++)
            r[i] -= a2b2[i];

        for (int i = 0; i < r.size(); i++)
            res[i + k] += r[i];
        for (int i = 0; i < a1b1.size(); i++)
            res[i] += a1b1[i];
        for (int i = 0; i < a2b2.size(); i++)
            res[i + n] += a2b2[i];
        return res;
    }

    bigint operator*(const bigint &v) const {
        vector<int> a6 = convert_base(this->z, base_digits, 6);
        vector<int> b6 = convert_base(v.z, base_digits, 6);
        vll a(a6.begin(), a6.end());
        vll b(b6.begin(), b6.end());
        while (a.size() < b.size())
            a.push_back(0);
        while (b.size() < a.size())
            b.push_back(0);
        while (a.size() & (a.size() - 1))
            a.push_back(0), b.push_back(0);
        vll c = karatsubaMultiply(a, b);
        bigint res;
        res.sign = sign * v.sign;
        for (int i = 0, carry = 0; i < c.size(); i++) {
            long long cur = c[i] + carry;
            res.z.push_back((int) (cur % 1000000));
            carry = (int) (cur / 1000000);
        }
        res.z = convert_base(res.z, 6, base_digits);
        res.trim();
        return res;
    }

};

bigint random_bigint(int n) {
    string s;
    for (int i = 0; i < n; i++) {
        s += rand() % 10 + '0';
    }
    return bigint(s);
}

// random tests
void bigintTest() {
    bigint x = bigint("120");
    bigint y = bigint("5");
    cout << x / y << endl;

    for (int i = 0; i < 1000; i++) {
        int n = rand() % 100 + 1;
        bigint a = random_bigint(n);
        bigint res = sqrt(a);
        bigint xx = res * res;
        bigint yy = (res + 1) * (res + 1);

        if (xx > a || yy <= a) {
            cout << i << endl;
            cout << a << " " << res << endl;
            break;
        }

        int m = rand() % n + 1;
        bigint b = random_bigint(m) + 1;
        res = a / b;
        xx = res * b;
        yy = b * (res + 1);

        if (xx > a || yy <= a) {
            cout << i << endl;
            cout << a << " " << b << " " << res << endl;
            break;
        }
    }

    bigint a = random_bigint(10000);
    bigint b = random_bigint(2000);
    clock_t start = clock();
    bigint c = a / b;
    printf("time=%.3lfsec\n", (clock() - start) * 1. / CLOCKS_PER_SEC);
}

string str(bigint b) {
    stringstream ss; ss << b;
    string s; ss >> s;
    return s;
}