結果

問題 No.2086 A+B問題
ユーザー anqooqie
提出日時 2022-11-05 20:21:15
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 56,387 bytes
コンパイル時間 3,283 ms
コンパイル使用メモリ 235,344 KB
最終ジャッジ日時 2025-02-08 18:47:11
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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ファイルパターン 結果
other AC * 21
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#line 1 "main.cpp"
#include <bits/stdc++.h>
#line 1 "/home/anqooqie/.proconlib/tools/bigint.hpp"
#line 10 "/home/anqooqie/.proconlib/tools/bigint.hpp"
#include <type_traits>
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"
#line 7 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_math.hpp"
#line 5 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_math.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;
    // @param m `1 <= m < 2^31`
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
    // @return m
    unsigned int umod() const { return _m; }
    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay
        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;
    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b
        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }
        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}
}  // namespace internal
}  // namespace atcoder
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_type_traits.hpp"
#line 7 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_type_traits.hpp"
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;
template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;
template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;
template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;
template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
}  // namespace internal
}  // namespace atcoder
#line 14 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/modint.hpp"
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
}  // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;
  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }
    unsigned int val() const { return _v; }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;
  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }
    unsigned int val() const { return _v; }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
}  // namespace internal
}  // namespace atcoder
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/convolution.hpp"
#line 9 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/convolution.hpp"
#line 1 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/internal_bit.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}
}  // namespace internal
}  // namespace atcoder
#line 12 "/home/anqooqie/.proconlib/lib/ac-library/atcoder/convolution.hpp"
namespace atcoder {
namespace internal {
template <class mint,
          int g = internal::primitive_root<mint::mod()>,
          internal::is_static_modint_t<mint>* = nullptr>
struct fft_info {
    static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);
    std::array<mint, rank2 + 1> root;   // root[i]^(2^i) == 1
    std::array<mint, rank2 + 1> iroot;  // root[i] * iroot[i] == 1
    std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
    std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;
    std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
    std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;
    fft_info() {
        root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
        iroot[rank2] = root[rank2].inv();
        for (int i = rank2 - 1; i >= 0; i--) {
            root[i] = root[i + 1] * root[i + 1];
            iroot[i] = iroot[i + 1] * iroot[i + 1];
        }
        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 2; i++) {
                rate2[i] = root[i + 2] * prod;
                irate2[i] = iroot[i + 2] * iprod;
                prod *= iroot[i + 2];
                iprod *= root[i + 2];
            }
        }
        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 3; i++) {
                rate3[i] = root[i + 3] * prod;
                irate3[i] = iroot[i + 3] * iprod;
                prod *= iroot[i + 3];
                iprod *= root[i + 3];
            }
        }
    }
};
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
    int n = int(a.size());
    int h = internal::ceil_pow2(n);
    static const fft_info<mint> info;
    int len = 0;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while (len < h) {
        if (h - len == 1) {
            int p = 1 << (h - len - 1);
            mint rot = 1;
            for (int s = 0; s < (1 << len); s++) {
                int offset = s << (h - len);
                for (int i = 0; i < p; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + p] * rot;
                    a[i + offset] = l + r;
                    a[i + offset + p] = l - r;
                }
                if (s + 1 != (1 << len))
                    rot *= info.rate2[bsf(~(unsigned int)(s))];
            }
            len++;
        } else {
            // 4-base
            int p = 1 << (h - len - 2);
            mint rot = 1, imag = info.root[2];
            for (int s = 0; s < (1 << len); s++) {
                mint rot2 = rot * rot;
                mint rot3 = rot2 * rot;
                int offset = s << (h - len);
                for (int i = 0; i < p; i++) {
                    auto mod2 = 1ULL * mint::mod() * mint::mod();
                    auto a0 = 1ULL * a[i + offset].val();
                    auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
                    auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
                    auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
                    auto a1na3imag =
                        1ULL * mint(a1 + mod2 - a3).val() * imag.val();
                    auto na2 = mod2 - a2;
                    a[i + offset] = a0 + a2 + a1 + a3;
                    a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
                    a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
                    a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
                }
                if (s + 1 != (1 << len))
                    rot *= info.rate3[bsf(~(unsigned int)(s))];
            }
            len += 2;
        }
    }
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
    int n = int(a.size());
    int h = internal::ceil_pow2(n);
    static const fft_info<mint> info;
    int len = h;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while (len) {
        if (len == 1) {
            int p = 1 << (h - len);
            mint irot = 1;
            for (int s = 0; s < (1 << (len - 1)); s++) {
                int offset = s << (h - len + 1);
                for (int i = 0; i < p; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + p];
                    a[i + offset] = l + r;
                    a[i + offset + p] =
                        (unsigned long long)(mint::mod() + l.val() - r.val()) *
                        irot.val();
                    ;
                }
                if (s + 1 != (1 << (len - 1)))
                    irot *= info.irate2[bsf(~(unsigned int)(s))];
            }
            len--;
        } else {
            // 4-base
            int p = 1 << (h - len);
            mint irot = 1, iimag = info.iroot[2];
            for (int s = 0; s < (1 << (len - 2)); s++) {
                mint irot2 = irot * irot;
                mint irot3 = irot2 * irot;
                int offset = s << (h - len + 2);
                for (int i = 0; i < p; i++) {
                    auto a0 = 1ULL * a[i + offset + 0 * p].val();
                    auto a1 = 1ULL * a[i + offset + 1 * p].val();
                    auto a2 = 1ULL * a[i + offset + 2 * p].val();
                    auto a3 = 1ULL * a[i + offset + 3 * p].val();
                    auto a2na3iimag =
                        1ULL *
                        mint((mint::mod() + a2 - a3) * iimag.val()).val();
                    a[i + offset] = a0 + a1 + a2 + a3;
                    a[i + offset + 1 * p] =
                        (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
                    a[i + offset + 2 * p] =
                        (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
                        irot2.val();
                    a[i + offset + 3 * p] =
                        (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
                        irot3.val();
                }
                if (s + 1 != (1 << (len - 2)))
                    irot *= info.irate3[bsf(~(unsigned int)(s))];
            }
            len -= 2;
        }
    }
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint>& a,
                                    const std::vector<mint>& b) {
    int n = int(a.size()), m = int(b.size());
    std::vector<mint> ans(n + m - 1);
    if (n < m) {
        for (int j = 0; j < m; j++) {
            for (int i = 0; i < n; i++) {
                ans[i + j] += a[i] * b[j];
            }
        }
    } else {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ans[i + j] += a[i] * b[j];
            }
        }
    }
    return ans;
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    int z = 1 << internal::ceil_pow2(n + m - 1);
    a.resize(z);
    internal::butterfly(a);
    b.resize(z);
    internal::butterfly(b);
    for (int i = 0; i < z; i++) {
        a[i] *= b[i];
    }
    internal::butterfly_inv(a);
    a.resize(n + m - 1);
    mint iz = mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
    return a;
}
}  // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(const std::vector<mint>& a,
                              const std::vector<mint>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}
template <unsigned int mod = 998244353,
          class T,
          std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    using mint = static_modint<mod>;
    std::vector<mint> a2(n), b2(m);
    for (int i = 0; i < n; i++) {
        a2[i] = mint(a[i]);
    }
    for (int i = 0; i < m; i++) {
        b2[i] = mint(b[i]);
    }
    auto c2 = convolution(move(a2), move(b2));
    std::vector<T> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        c[i] = c2[i].val();
    }
    return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
                                      const std::vector<long long>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    static constexpr unsigned long long MOD1 = 754974721;  // 2^24
    static constexpr unsigned long long MOD2 = 167772161;  // 2^25
    static constexpr unsigned long long MOD3 = 469762049;  // 2^26
    static constexpr unsigned long long M2M3 = MOD2 * MOD3;
    static constexpr unsigned long long M1M3 = MOD1 * MOD3;
    static constexpr unsigned long long M1M2 = MOD1 * MOD2;
    static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
    static constexpr unsigned long long i1 =
        internal::inv_gcd(MOD2 * MOD3, MOD1).second;
    static constexpr unsigned long long i2 =
        internal::inv_gcd(MOD1 * MOD3, MOD2).second;
    static constexpr unsigned long long i3 =
        internal::inv_gcd(MOD1 * MOD2, MOD3).second;
    auto c1 = convolution<MOD1>(a, b);
    auto c2 = convolution<MOD2>(a, b);
    auto c3 = convolution<MOD3>(a, b);
    std::vector<long long> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i] * i1) % MOD1 * M2M3;
        x += (c2[i] * i2) % MOD2 * M1M3;
        x += (c3[i] * i3) % MOD3 * M1M2;
        // B = 2^63, -B <= x, r(real value) < B
        // (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
        // r = c1[i] (mod MOD1)
        // focus on MOD1
        // r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
        // r = x,
        //     x - M' + (0 or 2B),
        //     x - 2M' + (0, 2B or 4B),
        //     x - 3M' + (0, 2B, 4B or 6B) (without mod!)
        // (r - x) = 0, (0)
        //           - M' + (0 or 2B), (1)
        //           -2M' + (0 or 2B or 4B), (2)
        //           -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
        // we checked that
        //   ((1) mod MOD1) mod 5 = 2
        //   ((2) mod MOD1) mod 5 = 3
        //   ((3) mod MOD1) mod 5 = 4
        long long diff =
            c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
        if (diff < 0) diff += MOD1;
        static constexpr unsigned long long offset[5] = {
            0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
        x -= offset[diff % 5];
        c[i] = x;
    }
    return c;
}
}  // namespace atcoder
#line 1 "/home/anqooqie/.proconlib/tools/quo.hpp"
#line 5 "/home/anqooqie/.proconlib/tools/quo.hpp"
namespace tools {
  template <typename M, typename N>
  constexpr ::std::common_type_t<M, N> quo(const M lhs, const N rhs) {
    if (lhs >= 0) {
      return lhs / rhs;
    } else {
      if (rhs >= 0) {
        return -((-lhs - 1 + rhs) / rhs);
      } else {
        return (-lhs - 1 + -rhs) / -rhs;
      }
    }
  }
}
#line 1 "/home/anqooqie/.proconlib/tools/mod.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/mod.hpp"
namespace tools {
  template <typename M, typename N>
  constexpr ::std::common_type_t<M, N> mod(const M lhs, const N rhs) {
    if constexpr (::std::is_unsigned_v<M> && ::std::is_unsigned_v<N>) {
      return lhs % rhs;
    } else {
      return lhs - ::tools::quo(lhs, rhs) * rhs;
    }
  }
}
#line 1 "/home/anqooqie/.proconlib/tools/floor.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/floor.hpp"
namespace tools {
  template <typename M, typename N>
  constexpr ::std::common_type_t<M, N> floor(const M lhs, const N rhs) {
    assert(rhs != 0);
    return lhs / rhs - (((lhs > 0 && rhs < 0) || (lhs < 0 && rhs > 0)) && lhs % rhs);
  }
}
#line 1 "/home/anqooqie/.proconlib/tools/ssize.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/ssize.hpp"
namespace tools {
  template <typename C>
  constexpr auto ssize(const C& c) -> ::std::common_type_t<::std::ptrdiff_t, ::std::make_signed_t<decltype(c.size())>> {
    return c.size();
  }
}
#line 1 "/home/anqooqie/.proconlib/tools/ceil.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/ceil.hpp"
namespace tools {
  template <typename M, typename N>
  constexpr ::std::common_type_t<M, N> ceil(const M lhs, const N rhs) {
    assert(rhs != 0);
    return lhs / rhs + (((lhs > 0 && rhs > 0) || (lhs < 0 && rhs < 0)) && lhs % rhs);
  }
}
#line 1 "/home/anqooqie/.proconlib/tools/garner2.hpp"
#line 1 "/home/anqooqie/.proconlib/tools/is_prime.hpp"
#line 1 "/home/anqooqie/.proconlib/tools/prod_mod.hpp"
namespace tools {
  template <typename T1, typename T2, typename T3>
  constexpr T3 prod_mod(const T1 x, const T2 y, const T3 m) {
    using u128 = unsigned __int128;
    u128 prod_mod = u128(x >= 0 ? x : -x) * u128(y >= 0 ? y : -y) % u128(m);
    if ((x >= 0) ^ (y >= 0)) prod_mod = u128(m) - prod_mod;
    return prod_mod;
  }
}
#line 1 "/home/anqooqie/.proconlib/tools/pow_mod.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/pow_mod.hpp"
namespace tools {
  template <typename T1, typename T2, typename T3>
  constexpr T3 pow_mod(const T1 x, T2 n, const T3 m) {
    if (m == 1) return 0;
    T3 r = 1;
    T3 y = ::tools::mod(x, m);
    while (n > 0) {
      if ((n & 1) > 0) {
        r = ::tools::prod_mod(r, y, m);
      }
      y = ::tools::prod_mod(y, y, m);
      n /= 2;
    }
    return r;
  }
}
#line 7 "/home/anqooqie/.proconlib/tools/is_prime.hpp"
namespace tools {
  constexpr bool is_prime(const ::std::uint_fast64_t n) {
    constexpr ::std::array<unsigned long long, 7> bases = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
    if (n <= 1) return false;
    if (n == 2) return true;
    if (n % 2 == 0) return false;
    auto d = n - 1;
    for (; d % 2 == 0; d /= 2);
    for (const auto a : bases) {
      if (a % n == 0) return true;
      auto power = d;
      auto target = ::tools::pow_mod(a, power, n);
      bool is_composite = true;
      if (target == 1) is_composite = false;
      for (; is_composite && power != n - 1; power *= 2, target = ::tools::prod_mod(target, target, n)) {
        if (target == n - 1) is_composite = false;
      }
      if (is_composite) {
        return false;
      }
    }
    return true;
  }
}
#line 6 "/home/anqooqie/.proconlib/tools/garner2.hpp"
namespace tools {
  template <typename M1, typename M2>
  long long garner2(const M1& a, const M2& b) {
    using ull = unsigned long long;
    static constexpr ull m1_m2 = ull(M1::mod()) * ull(M2::mod());
    static const M2 m1_inv_mod_m2 = M2::raw(M1::mod()).inv();
    assert(M1::mod() < M2::mod());
    assert(::tools::is_prime(M1::mod()));
    assert(::tools::is_prime(M2::mod()));
    // t = (b - a) / M1; (mod M2)
    // return a + t * M1;
    const M2 t = (b - M2::raw(a.val())) * m1_inv_mod_m2;
    ull r = t.val();
    r *= M1::mod();
    r += a.val();
    if (r >= m1_m2) r -= m1_m2;
    return r;
  }
}
#line 1 "/home/anqooqie/.proconlib/tools/pow2.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/pow2.hpp"
namespace tools {
  template <typename T, typename ::std::enable_if<::std::is_unsigned<T>::value, ::std::nullptr_t>::type = nullptr>
  constexpr T pow2(const T x) {
    return static_cast<T>(1) << x;
  }
  template <typename T, typename ::std::enable_if<::std::is_signed<T>::value, ::std::nullptr_t>::type = nullptr>
  constexpr T pow2(const T x) {
    return static_cast<T>(static_cast<typename ::std::make_unsigned<T>::type>(1) << static_cast<typename ::std::make_unsigned<T>::type>(x));
  }
}
#line 1 "/home/anqooqie/.proconlib/tools/abs.hpp"
namespace tools {
  constexpr float abs(const float x) {
    return x < 0 ? -x : x;
  }
  constexpr double abs(const double x) {
    return x < 0 ? -x : x;
  }
  constexpr long double abs(const long double x) {
    return x < 0 ? -x : x;
  }
  constexpr int abs(const int x) {
    return x < 0 ? -x : x;
  }
  constexpr long abs(const long x) {
    return x < 0 ? -x : x;
  }
  constexpr long long abs(const long long x) {
    return x < 0 ? -x : x;
  }
}
#line 1 "/home/anqooqie/.proconlib/tools/gcd.hpp"
#line 6 "/home/anqooqie/.proconlib/tools/gcd.hpp"
namespace tools {
  template <typename M, typename N>
  constexpr ::std::common_type_t<M, N> gcd(const M m, const N n) {
    return ::std::gcd(m, n);
  }
}
#line 29 "/home/anqooqie/.proconlib/tools/bigint.hpp"
namespace tools {
  class bigint {
  private:
    using mint1 = ::atcoder::static_modint<167772161>;
    using mint2 = ::atcoder::static_modint<469762049>;
    bool m_positive;
    ::std::vector<::std::int_fast32_t> m_digits;
    static constexpr ::std::int_fast32_t BASE = 10000;
    static constexpr ::std::int_fast32_t LOG10_BASE = 4;
    static constexpr ::std::array<::std::int_fast32_t, 5> POW10 = {1, 10, 100, 1000, 10000};
    static int compare_3way(const ::std::size_t lhs, const ::std::size_t rhs) {
      if (lhs < rhs) return -1;
      if (lhs == rhs) return 0;
      return 1;
    }
    static int compare_3way_abs(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
      if (const auto comp = ::tools::bigint::compare_3way(lhs.m_digits.size(), rhs.m_digits.size()); comp != 0) {
        return comp;
      }
      for (::std::size_t i = 0; i < lhs.m_digits.size(); ++i) {
        if (const auto comp = ::tools::bigint::compare_3way(lhs.m_digits[lhs.m_digits.size() - 1 - i], rhs.m_digits[rhs.m_digits.size() - 1 - i]); 
            comp != 0) {
          return comp;
        }
      }
      return 0;
    }
    ::tools::bigint& regularize(const int level) {
      if (level > 0) {
        if (level == 2) {
          for (::std::size_t i = 0; i + 1 < this->m_digits.size(); ++i) {
            this->m_digits[i + 1] += ::tools::quo(this->m_digits[i], BASE);
            this->m_digits[i] = ::tools::mod(this->m_digits[i], BASE);
          }
        } else {
          for (::std::size_t i = 0; i + 1 < this->m_digits.size(); ++i) {
            if (this->m_digits[i] < 0) {
              this->m_digits[i] += BASE;
              --this->m_digits[i + 1];
            } else if (this->m_digits[i] >= BASE) {
              this->m_digits[i] -= BASE;
              ++this->m_digits[i + 1];
            }
          }
        }
        if (!this->m_digits.empty() && this->m_digits.back() < 0) {
          this->m_positive = !this->m_positive;
          for (::std::size_t i = 0; i < this->m_digits.size(); ++i) {
            this->m_digits[i] = -this->m_digits[i];
          }
          for (::std::size_t i = 0; i + 1 < this->m_digits.size(); ++i) {
            if (this->m_digits[i] < 0) {
              this->m_digits[i] = BASE + this->m_digits[i];
              --this->m_digits[i + 1];
            }
          }
        }
        if (level == 2) {
          while (!this->m_digits.empty() && this->m_digits.back() >= BASE) {
            this->m_digits.push_back(this->m_digits.back() / BASE);
            this->m_digits[this->m_digits.size() - 2] %= BASE;
          }
        } else {
          if (!this->m_digits.empty() && this->m_digits.back() >= BASE) {
            this->m_digits.back() -= BASE;
            this->m_digits.push_back(1);
          }
        }
      }
      while (!this->m_digits.empty() && this->m_digits.back() == 0) {
        this->m_digits.pop_back();
      }
      if (this->m_digits.empty() && !this->m_positive) {
        this->m_positive = true;
      }
      return *this;
    }
  public:
    ::tools::bigint& negate() {
      if (!this->m_digits.empty()) {
        this->m_positive = !this->m_positive;
      }
      return *this;
    }
    ::tools::bigint& multiply_by_pow10(const ::std::ptrdiff_t exponent) {
      if (!this->m_digits.empty()) {
        const ::std::ptrdiff_t exponent10000 = ::tools::floor(exponent, LOG10_BASE);
        ::std::int_fast32_t mod = 0;
        if (exponent10000 > 0) {
          ::std::vector<::std::int_fast32_t> zero(exponent10000, 0);
          this->m_digits.insert(this->m_digits.begin(), zero.begin(), zero.end());
        } else if (exponent10000 < 0) {
          if (::tools::ssize(this->m_digits) >= -exponent10000) {
            mod = this->m_digits[-exponent10000 - 1] / POW10[LOG10_BASE * (exponent10000 + 1) - exponent];
          }
          this->m_digits.erase(this->m_digits.begin(), this->m_digits.begin() + ::std::min<::std::size_t>(-exponent10000, this->m_digits.size()));
        }
        if (const ::std::int_fast32_t coefficient = POW10[exponent - LOG10_BASE * exponent10000]; coefficient > POW10[0]) {
          for (auto& d : this->m_digits) {
            d *= coefficient;
          }
          if (mod > 0 && this->m_digits.empty()) {
            this->m_digits.push_back(0);
          }
          this->m_digits[0] += mod;
          this->regularize(2);
        } else {
          this->regularize(0);
        }
      }
      return *this;
    }
    ::tools::bigint& divide_by_pow10(const ::std::ptrdiff_t exponent) {
      this->multiply_by_pow10(-exponent);
      return *this;
    }
    static int compare_3way(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
      if (!lhs.m_positive && rhs.m_positive) return -1;
      if (lhs.m_positive && !rhs.m_positive) return 1;
      return ::tools::bigint::compare_3way_abs(lhs, rhs) * (lhs.m_positive ? 1 : -1);
    }
    int signum() const {
      if (!this->m_positive) return -1;
      if (this->m_digits.empty()) return 0;
      return 1;
    }
    ::std::size_t size() const {
      if (this->m_digits.empty()) return 0;
      return LOG10_BASE * (this->m_digits.size() - 1) + ::std::distance(POW10.begin(), ::std::upper_bound(POW10.begin(), POW10.end(), this
          ->m_digits[this->m_digits.size() - 1]));
    }
    ::std::int_fast32_t operator[](const ::std::size_t i) const {
      return i < LOG10_BASE * this->m_digits.size() ? this->m_digits[i / LOG10_BASE] / POW10[i % LOG10_BASE] % 10 : 0;
    }
  private:
    ::tools::bigint& internal_add(const ::tools::bigint& other, const bool plus) {
      const bool this_positive = this->m_positive;
      if (!this_positive) {
        this->negate();
      }
      this->m_digits.resize(::std::max(this->m_digits.size(), other.m_digits.size()));
      if (this_positive == (other.m_positive == plus)) {
        for (::std::size_t i = 0; i < other.m_digits.size(); ++i) {
          this->m_digits[i] += other.m_digits[i];
        }
      } else {
        for (::std::size_t i = 0; i < other.m_digits.size(); ++i) {
          this->m_digits[i] -= other.m_digits[i];
        }
      }
      this->regularize(1);
      if (!this_positive) {
        this->negate();
      }
      return *this;
    }
  public:
    bigint() : m_positive(true) {
    }
    bigint(const ::tools::bigint&) = default;
    bigint(::tools::bigint&&) = default;
    ~bigint() = default;
    ::tools::bigint& operator=(const ::tools::bigint&) = default;
    ::tools::bigint& operator=(::tools::bigint&&) = default;
    template <typename T, typename ::std::enable_if<::std::is_integral_v<T>, ::std::nullptr_t>::type = nullptr>
    explicit bigint(T n) : m_positive(n >= 0) {
      while (n != 0) {
        this->m_digits.push_back(n % BASE);
        n /= BASE;
      }
      if (!this->m_positive) {
        for (auto& d : this->m_digits) {
          d = -d;
        }
      }
    }
    explicit bigint(const ::std::string& s) {
      assert(!s.empty());
      ::std::size_t offset;
      if (s[0] == '+') {
        this->m_positive = true;
        offset = 1;
      } else if (s[0] == '-') {
        this->m_positive = false;
        offset = 1;
      } else {
        this->m_positive = true;
        offset = 0;
      }
      this->m_digits.reserve(::tools::ceil<::std::size_t>(s.size() - offset, LOG10_BASE));
      for (::std::size_t i = 0; i < s.size() - offset; i += LOG10_BASE) {
        this->m_digits.push_back(0);
        for (::std::size_t j = ::std::min(i + LOG10_BASE, s.size() - offset); j --> i;) {
          assert('0' <= s[s.size() - 1 - j] && s[s.size() - 1 - j] <= '9');
          this->m_digits.back() = this->m_digits.back() * 10 + (s[s.size() - 1 - j] - '0');
        }
      }
      this->regularize(0);
    }
    friend bool operator==(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
      return lhs.m_positive == rhs.m_positive && lhs.m_digits == rhs.m_digits;
    }
    friend bool operator!=(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
      return !(lhs == rhs);
    }
    friend bool operator<(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
      return ::tools::bigint::compare_3way(lhs, rhs) < 0;
    }
    friend bool operator>(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
      return ::tools::bigint::compare_3way(lhs, rhs) > 0;
    }
    friend bool operator<=(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
      return ::tools::bigint::compare_3way(lhs, rhs) <= 0;
    }
    friend bool operator>=(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
      return ::tools::bigint::compare_3way(lhs, rhs) >= 0;
    }
    ::tools::bigint operator+() const {
      return *this;
    }
    ::tools::bigint operator-() const {
      return ::tools::bigint(*this).negate();
    }
    ::tools::bigint& operator+=(const ::tools::bigint& other) {
      return this->internal_add(other, true);
    }
    ::tools::bigint& operator-=(const ::tools::bigint& other) {
      return this->internal_add(other, false);
    }
    ::tools::bigint& operator*=(const ::tools::bigint& other) {
      // Constraint derived from atcoder::convolution
      assert(this->m_digits.size() + other.m_digits.size() <= ::tools::pow2(25) + 1);
      ::std::vector<mint1> a1, b1;
      ::std::vector<mint2> a2, b2;
      a1.reserve(this->m_digits.size());
      a2.reserve(this->m_digits.size());
      b1.reserve(other.m_digits.size());
      b2.reserve(other.m_digits.size());
      for (const auto a_i : this->m_digits) {
        a1.push_back(mint1::raw(a_i));
        a2.push_back(mint2::raw(a_i));
      }
      for (const auto b_i : other.m_digits) {
        b1.push_back(mint1::raw(b_i));
        b2.push_back(mint2::raw(b_i));
      }
      const auto c1 = ::atcoder::convolution(a1, b1);
      const auto c2 = ::atcoder::convolution(a2, b2);
      this->m_digits.clear();
      this->m_digits.reserve(c1.size() + 1);
      long long carry = 0;
      for (::std::size_t i = 0; i < c1.size(); ++i) {
        // Since a_i <= 10^4 - 1 and b_i <= 10^4 - 1, c_i <= (10^4 - 1)^2 * min(this->m_digits.size(), other.m_digits.size()) holds.
        // In addition, since this->m_digits.size() + other.m_digits.size() <= 2^25 + 1, c_i <= (10^4 - 1)^2 * 2^24 = 1677386072457216 holds 
            eventually.
        // 1677386072457216 < 167772161 * 469762049 = 78812994116517889 holds, so we can reconstruct c_i from mod(c_i, 167772161) and mod(c_i, 
            469762049) by CRT.
        long long c_i = ::tools::garner2(c1[i], c2[i]);
        c_i += carry;
        carry = c_i / BASE;
        c_i %= BASE;
        this->m_digits.push_back(c_i);
      }
      if (carry > 0) {
        this->m_digits.push_back(carry);
      }
      this->m_positive = this->m_positive == other.m_positive;
      this->regularize(0);
      return *this;
    }
    friend ::tools::bigint operator+(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
      return ::tools::bigint(lhs) += rhs;
    }
    friend ::tools::bigint operator-(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
      return ::tools::bigint(lhs) -= rhs;
    }
    friend ::tools::bigint operator*(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
      return ::tools::bigint(lhs) *= rhs;
    }
    ::tools::bigint& operator++() {
      return *this += ::tools::bigint(1);
    }
    ::tools::bigint operator++(int) {
      ::tools::bigint old(*this);
      ++(*this);
      return old;
    }
    ::tools::bigint& operator--() {
      return *this -= ::tools::bigint(1);
    }
    ::tools::bigint operator--(int) {
      ::tools::bigint old(*this);
      --(*this);
      return old;
    }
    ::tools::bigint& operator/=(const ::tools::bigint& other) {
      assert(other.signum() != 0);
      if (::tools::bigint::compare_3way_abs(*this, other) < 0) {
        this->m_digits.clear();
        this->m_positive = true;
        return *this;
      }
      if (other.m_digits.size() == 1 && other.m_digits[0] == 1) {
        this->m_positive = (this->m_positive == other.m_positive);
        return *this;
      }
      using u64 = ::std::uint_fast64_t;
      static const ::tools::bigint u64_threshold((::std::numeric_limits<u64>::max() - (BASE - 1)) / BASE);
      using u128 = unsigned __int128;
      static const ::tools::bigint u128_threshold("34028236692093846346337460743176820");
      #define TOOLS_BIGINT_NAIVE(type) do {\
        if (::tools::bigint::compare_3way_abs(other, type ## _threshold) <= 0) { \
          type mod = 0;\
          for (::std::size_t i = other.m_digits.size(); i --> 0;) {\
            mod *= BASE;\
            mod += other.m_digits[i];\
          }\
          \
          type carry = 0;\
          for (::std::size_t i = this->m_digits.size(); i--> 0;) {\
            carry *= BASE;\
            carry += this->m_digits[i];\
            this->m_digits[i] = carry / mod;\
            carry %= mod;\
          }\
          \
          this->m_positive = (this->m_positive == other.m_positive);\
          return this->regularize(0);\
        }\
      } while (false)
      TOOLS_BIGINT_NAIVE(u64);
      TOOLS_BIGINT_NAIVE(u128);
      #undef TOOLS_BIGINT_NAIVE
      using bigdecimal = ::std::pair<::tools::bigint, ::std::ptrdiff_t>;
      static const auto precision = [](const bigdecimal& x) {
        return x.first.m_digits.size();
      };
      static const auto regularize = [](bigdecimal& x) -> bigdecimal& {
        if (x.first.m_digits.empty()) {
          x.second = 0;
        }
        return x;
      };
      static const auto negate = [](bigdecimal& x) -> bigdecimal& {
        x.first.negate();
        return x;
      };
      static const auto make_abs = [](bigdecimal& x) -> bigdecimal& {
        if (!x.first.m_positive) {
          negate(x);
        }
        return x;
      };
      static const auto set_precision = [](bigdecimal& x, const ::std::size_t p) -> bigdecimal& {
        const ::std::ptrdiff_t diff = ::std::ptrdiff_t(p) - ::std::ptrdiff_t(precision(x));
        x.first.multiply_by_pow10(diff * LOG10_BASE);
        x.second -= diff;
        regularize(x);
        return x;
      };
      static const auto plus = [](bigdecimal& x, bigdecimal& y) -> bigdecimal& {
        if (x.second < y.second) {
          set_precision(y, precision(y) + (y.second - x.second));
        } else if (x.second > y.second) {
          set_precision(x, precision(x) + (x.second - y.second));
        }
        x.first += y.first;
        regularize(x);
        return x;
      };
      static const auto multiplies = [](bigdecimal& x, const bigdecimal& y) -> bigdecimal& {
        x.first *= y.first;
        x.second += y.second;
        regularize(x);
        return x;
      };
      static const auto compare_3way = [](const bigdecimal& x, const bigdecimal& y) {
        if (!x.first.m_positive && y.first.m_positive) return -1;
        if (x.first.m_positive && !y.first.m_positive) return 1;
        return [&]() {
          if (x.second <= y.second) {
            if (const auto comp = ::tools::bigint::compare_3way(precision(x), precision(y) + (y.second - x.second)); comp != 0) {
              return comp;
            }
            for (::std::size_t i = 0; i < precision(x); ++i) {
              if (const auto comp = ::tools::bigint::compare_3way(x.first.m_digits[precision(x) - 1 - i], precision(y) >= i + 1 ? y.first
                  .m_digits[precision(y) - 1 - i] : 0); comp != 0) {
                return comp;
              }
            }
          } else {
            if (const auto comp = ::tools::bigint::compare_3way(precision(x) + (x.second - y.second), precision(y)); comp != 0) {
              return comp;
            }
            for (::std::size_t i = 0; i < precision(y); ++i) {
              if (const auto comp = ::tools::bigint::compare_3way(precision(x) >= i + 1 ? x.first.m_digits[precision(x) - 1 - i] : 0, y.first
                  .m_digits[precision(y) - 1 - i]); comp != 0) {
                return comp;
              }
            }
          }
          return 0;
        }() * (x.first.m_positive ? 1 : -1);
      };
      const bool r_positive = this->m_positive == other.m_positive;
      if (!this->m_positive) {
        this->negate();
      }
      const ::std::size_t inv_final_goal_precision = this->m_digits.size() - other.m_digits.size() + 2;
      const ::std::size_t inv_first_goal_precision = ::std::min<::std::size_t>(inv_final_goal_precision, 3);
      bigdecimal o(other, 0);
      make_abs(o);
      set_precision(o, ::std::min<::std::size_t>(other.m_digits.size(), 6));
      bigdecimal prev_inv(::tools::bigint(0), 0);
      bigdecimal inv(::tools::bigint(1), -::tools::ssize(other.m_digits));
      while (compare_3way(prev_inv, inv) != 0) {
        prev_inv = inv;
        negate(inv);
        multiplies(inv, o);
        bigdecimal two(::tools::bigint(2), 0);
        plus(inv, two);
        multiplies(inv, prev_inv);
        set_precision(inv, ::std::min(precision(inv), inv_first_goal_precision));
      }
      if (inv_first_goal_precision < inv_final_goal_precision) {
        prev_inv = bigdecimal(::tools::bigint(0), 0);
        while (compare_3way(prev_inv, inv) != 0) {
          prev_inv = inv;
          negate(inv);
          multiplies(inv, o);
          bigdecimal two(::tools::bigint(2), 0);
          plus(inv, two);
          multiplies(inv, prev_inv);
          set_precision(inv, ::std::min(precision(prev_inv) * 2, inv_final_goal_precision));
          const ::std::size_t o_precision = precision(o);
          o = bigdecimal(other, 0);
          make_abs(o);
          set_precision(o, ::std::min(o_precision * 2, other.m_digits.size()));
        }
      }
      set_precision(inv, inv_final_goal_precision);
      o = bigdecimal(other, 0);
      make_abs(o);
      bigdecimal r(*this, 0);
      multiplies(r, inv);
      set_precision(r, precision(r) + r.second);
      ::tools::bigint r_plus_1 = r.first + ::tools::bigint(1);
      if (*this >= r_plus_1 * o.first) {
        *this = ::std::move(r_plus_1);
      } else {
        *this = ::std::move(r.first);
      }
      this->m_positive = r_positive;
      return *this;
    }
    friend ::tools::bigint operator/(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
      return ::tools::bigint(lhs) /= rhs;
    }
    ::tools::bigint& operator%=(const ::tools::bigint& other) {
      using u64 = ::std::uint_fast64_t;
      static const ::tools::bigint u64_threshold((::std::numeric_limits<u64>::max() - (BASE - 1)) / BASE);
      using u128 = unsigned __int128;
      static const ::tools::bigint u128_threshold("34028236692093846346337460743176820");
      #define TOOLS_BIGINT_NAIVE(type) do {\
        if (::tools::bigint::compare_3way_abs(other, type ## _threshold) <= 0) { \
          type mod = 0;\
          for (::std::size_t i = other.m_digits.size(); i --> 0;) {\
            mod *= BASE;\
            mod += other.m_digits[i];\
          }\
          \
          type result = 0;\
          for (::std::size_t i = this->m_digits.size(); i --> 0;) {\
            result *= BASE;\
            result += this->m_digits[i];\
            result %= mod;\
          }\
          \
          this->m_digits.clear();\
          while (result > 0) {\
            this->m_digits.push_back(result % BASE);\
            result /= BASE;\
          }\
          \
          return this->regularize(0);\
        }\
      } while (false)
      TOOLS_BIGINT_NAIVE(u64);
      TOOLS_BIGINT_NAIVE(u128);
      #undef TOOLS_BIGINT_NAIVE
      const ::tools::bigint self = *this;
      *this /= other;
      this->negate();
      *this *= other;
      *this += self;
      return *this;
    }
    friend ::tools::bigint operator%(const ::tools::bigint& lhs, const ::tools::bigint& rhs) {
      return ::tools::bigint(lhs) %= rhs;
    }
    template <typename T, ::std::enable_if_t<::std::is_integral_v<T>, ::std::nullptr_t> = nullptr>
    explicit operator T() const {
      assert(::tools::bigint(::std::numeric_limits<T>::min()) <= *this && *this <= ::tools::bigint(::std::numeric_limits<T>::max()));
      T result = 0;
      for (::std::size_t i = this->m_digits.size(); i --> 0;) {
        result = result * BASE + this->m_digits[i] * (this->m_positive ? 1 : -1);
      }
      return result;
    }
    explicit operator double() const {
      long double result = 0.0;
      const ::std::size_t precision = this->size();
      for (::std::size_t i = 0; i < ::std::numeric_limits<long double>::digits10; ++i) {
        result = result * 10.0L + (precision >= i + 1 ? (*this)[precision - 1 - i] : 0) * this->signum();
      }
      result *= ::std::pow(10.0L, static_cast<long double>(precision) - static_cast<long double>(::std::numeric_limits<long double>::digits10));
      return static_cast<double>(result);
    }
    friend ::std::istream& operator>>(::std::istream& is, ::tools::bigint& self) {
      ::std::string s;
      is >> s;
      self = ::tools::bigint(s);
      return is;
    }
    friend ::std::ostream& operator<<(::std::ostream& os, const ::tools::bigint& self) {
      if (!self.m_positive) {
        os << '-';
      }
      if (self.m_digits.empty()) {
        return os << '0';
      }
      os << self.m_digits.back();
      for (::std::size_t i = 1; i < self.m_digits.size(); ++i) {
        os << ::std::setw(LOG10_BASE) << ::std::setfill('0') << self.m_digits[self.m_digits.size() - 1 - i];
      }
      return os;
    }
    friend ::tools::bigint abs(::tools::bigint x);
  };
  inline ::tools::bigint abs(::tools::bigint x) {
    if (!x.m_positive) x.negate();
    return x;
  }
  inline ::tools::bigint gcd(::tools::bigint x, ::tools::bigint y) {
    if (x.signum() < 0) x.negate();
    if (y.signum() < 0) y.negate();
    while (y.signum() != 0) {
      x %= y;
      ::std::swap(x, y);
    }
    return x;
  }
}
#line 3 "main.cpp"
int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);
  tools::bigint A, B;
  std::cin >> A >> B;
  std::cout << A + B << '\n';
  return 0;
}
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