結果

問題 No.1781 LCM
ユーザー NyaanNyaanNyaanNyaan
提出日時 2021-12-20 21:31:46
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 521 ms / 5,000 ms
コード長 19,035 bytes
コンパイル時間 2,893 ms
コンパイル使用メモリ 262,432 KB
実行使用メモリ 9,696 KB
最終ジャッジ日時 2024-11-15 22:23:18
合計ジャッジ時間 7,263 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,816 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 2 ms
6,816 KB
testcase_03 AC 2 ms
6,816 KB
testcase_04 AC 2 ms
6,820 KB
testcase_05 AC 2 ms
6,820 KB
testcase_06 AC 2 ms
6,816 KB
testcase_07 AC 2 ms
6,820 KB
testcase_08 AC 2 ms
6,816 KB
testcase_09 AC 2 ms
6,816 KB
testcase_10 AC 2 ms
6,816 KB
testcase_11 AC 2 ms
6,820 KB
testcase_12 AC 2 ms
6,816 KB
testcase_13 AC 2 ms
6,816 KB
testcase_14 AC 2 ms
6,820 KB
testcase_15 AC 2 ms
6,820 KB
testcase_16 AC 2 ms
6,816 KB
testcase_17 AC 2 ms
6,816 KB
testcase_18 AC 2 ms
6,816 KB
testcase_19 AC 2 ms
6,816 KB
testcase_20 AC 2 ms
6,824 KB
testcase_21 AC 521 ms
9,580 KB
testcase_22 AC 517 ms
9,696 KB
testcase_23 AC 2 ms
6,820 KB
testcase_24 AC 2 ms
6,820 KB
testcase_25 AC 519 ms
9,472 KB
testcase_26 AC 518 ms
9,600 KB
testcase_27 AC 515 ms
9,600 KB
testcase_28 AC 436 ms
8,832 KB
testcase_29 AC 112 ms
6,816 KB
testcase_30 AC 116 ms
6,820 KB
testcase_31 AC 2 ms
6,816 KB
testcase_32 AC 2 ms
6,820 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

/**
 *  date : 2021-12-20 21:31:32
 */

#define NDEBUG
#define PROBLEM "https://yukicoder.me/problems/no/1781"
//
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  T &x() { return first; }
  const T &x() const { return first; }
  U &y() { return second; }
  const U &y() const { return second; }

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }

  P operator*(const P &r) const { return P(*this) *= r; }

  P operator*(int r) const { return {first * r, second * r}; }

  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

}  // namespace Nyaan

// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan

// inout
namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &... u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &... u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &... u) {
  cout << t;
  outr(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan

// debug
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (void(0))
#endif

// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }

//

// Prime Sieve {2, 3, 5, 7, 11, 13, 17, ...}
vector<int> prime_enumerate(int N) {
  vector<bool> sieve(N / 3 + 1, 1);
  for (int p = 5, d = 4, i = 1, sqn = sqrt(N); p <= sqn; p += d = 6 - d, i++) {
    if (!sieve[i]) continue;
    for (int q = p * p / 3, r = d * p / 3 + (d * p % 3 == 2), s = 2 * p,
             qe = sieve.size();
         q < qe; q += r = s - r)
      sieve[q] = 0;
  }
  vector<int> ret{2, 3};
  for (int p = 5, d = 4, i = 1; p <= N; p += d = 6 - d, i++)
    if (sieve[i]) ret.push_back(p);
  while (!ret.empty() && ret.back() > N) ret.pop_back();
  return ret;
}


using namespace Nyaan;




template <uint32_t mod>
struct LazyMontgomeryModInt {
  using mint = LazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static constexpr u32 r = get_r();
  static constexpr u32 n2 = -u64(mod) % mod;
  static_assert(r * mod == 1, "invalid, r * mod != 1");
  static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");

  u32 a;

  constexpr LazyMontgomeryModInt() : a(0) {}
  constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

  static constexpr u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }

  constexpr mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  constexpr mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
  constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
  constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
  constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
  constexpr bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr mint operator-() const { return mint() - mint(*this); }

  constexpr mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  
  constexpr mint inverse() const { return pow(mod - 2); }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = LazyMontgomeryModInt<mod>(t);
    return (is);
  }
  
  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static constexpr u32 get_mod() { return mod; }
};

template <typename T>
struct Binomial {
  vector<T> f, g, h;
  Binomial(int MAX = 0) : f(1, T(1)), g(1, T(1)), h(1, T(1)) {
    while (MAX >= (int)f.size()) extend();
  }

  void extend() {
    int n = f.size();
    int m = n * 2;
    f.resize(m);
    g.resize(m);
    h.resize(m);
    for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i);
    g[m - 1] = f[m - 1].inverse();
    h[m - 1] = g[m - 1] * f[m - 2];
    for (int i = m - 2; i >= n; i--) {
      g[i] = g[i + 1] * T(i + 1);
      h[i] = g[i] * f[i - 1];
    }
  }

  T fac(int i) {
    if (i < 0) return T(0);
    while (i >= (int)f.size()) extend();
    return f[i];
  }

  T finv(int i) {
    if (i < 0) return T(0);
    while (i >= (int)g.size()) extend();
    return g[i];
  }

  T inv(int i) {
    if (i < 0) return -inv(-i);
    while (i >= (int)h.size()) extend();
    return h[i];
  }

  T C(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r) * finv(r);
  }

  inline T operator()(int n, int r) { return C(n, r); }

  template <typename I>
  T multinomial(const vector<I>& r) {
    static_assert(is_integral<I>::value == true);
    int n = 0;
    for (auto& x : r) {
      if(x < 0) return T(0);
      n += x;
    }
    T res = fac(n);
    for (auto& x : r) res *= finv(x);
    return res;
  }

  template <typename I>
  T operator()(const vector<I>& r) {
    return multinomial(r);
  }

  T C_naive(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    T ret = T(1);
    r = min(r, n - r);
    for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);
    return ret;
  }

  T P(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r);
  }

  T H(int n, int r) {
    if (n < 0 || r < 0) return T(0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};



// f(p, c) : f(p^c) の値を返す
template <typename T, T (*f)(long long, long long)>
struct mf_prefix_sum {
  using i64 = long long;

  i64 M, sq, s;
  vector<int> p;
  int ps;
  vector<T> buf;
  T ans;

  mf_prefix_sum(i64 m) : M(m) {
    assert(m < (1LL << 42));
    sq = sqrt(M);
    while (sq * sq > M) sq--;
    while ((sq + 1) * (sq + 1) <= M) sq++;

    if (M != 0) {
      i64 hls = md(M, sq);
      if (hls != 1 && md(M, hls - 1) == sq) hls--;
      s = hls + sq;

      p = prime_enumerate(sq);
      ps = p.size();
      ans = T{};
    }
  }

  // 素数の個数関数に関するテーブル
  vector<T> pi_table() {
    if (M == 0) return {};
    i64 hls = md(M, sq);
    if (hls != 1 && md(M, hls - 1) == sq) hls--;

    vector<i64> hl(hls);
    for (int i = 1; i < hls; i++) hl[i] = md(M, i) - 1;

    vector<int> hs(sq + 1);
    iota(begin(hs), end(hs), -1);

    int pi = 0;
    for (auto& x : p) {
      i64 x2 = i64(x) * x;
      i64 imax = min<i64>(hls, md(M, x2) + 1);
      for (i64 i = 1, ix = x; i < imax; ++i, ix += x) {
        hl[i] -= (ix < hls ? hl[ix] : hs[md(M, ix)]) - pi;
      }
      for (int n = sq; n >= x2; n--) hs[n] -= hs[md(n, x)] - pi;
      pi++;
    }

    vector<T> res;
    res.reserve(2 * sq + 10);
    for (auto& x : hl) res.push_back(x);
    for (int i = hs.size(); --i;) res.push_back(hs[i]);
    assert((int)res.size() == s);
    return res;
  }

  // 素数の prefix sum に関するテーブル
  vector<T> prime_sum_table() {
    if (M == 0) return {};
    i64 hls = md(M, sq);
    if (hls != 1 && md(M, hls - 1) == sq) hls--;

    vector<T> h(s);
    T inv2 = T{2}.inverse();
    for (int i = 1; i < hls; i++) {
      T x = md(M, i);
      h[i] = x * (x + 1) * inv2 - 1;
    }
    for (int i = 1; i <= sq; i++) {
      T x = i;
      h[s - i] = x * (x + 1) / 2 - 1;
    }

    for (auto& x : p) {
      T xt = x;
      T pi = h[s - x + 1];
      i64 x2 = i64(x) * x;
      i64 imax = min<i64>(hls, md(M, x2) + 1);
      i64 ix = x;
      for (i64 i = 1; i < imax; ++i, ix += x) {
        h[i] -= ((ix < hls ? h[ix] : h[s - md(M, ix)]) - pi) * xt;
      }
      for (int n = sq; n >= x2; n--) {
        h[s - n] -= (h[s - md(n, x)] - pi) * xt;
      }
    }

    assert((int)h.size() == s);
    return h;
  }

  void dfs(int i, int c, i64 prod, T cur) {
    ans += cur * f(p[i], c + 1);
    i64 lim = md(M, prod);
    if (lim >= 1LL * p[i] * p[i]) dfs(i, c + 1, p[i] * prod, cur);
    cur *= f(p[i], c);
    ans += cur * (buf[idx(lim)] - buf[idx(p[i])]);
    int j = i + 1;
    // M < 2**42 -> p_j < 2**21 -> (p_j)^3 < 2**63
    for (; j < ps && 1LL * p[j] * p[j] * p[j] <= lim; j++) {
      dfs(j, 1, prod * p[j], cur);
    }
    for (; j < ps && 1LL * p[j] * p[j] <= lim; j++) {
      T sm = f(p[j], 2);
      int id1 = idx(md(lim, p[j])), id2 = idx(p[j]);
      sm += f(p[j], 1) * (buf[id1] - buf[id2]);
      ans += cur * sm;
    }
  }

  // fprime 破壊的
  T run(vector<T>& fprime) {
    if (M == 0) return {};
    set_buf(fprime);
    assert((int)buf.size() == s);
    ans = buf[idx(M)] + 1;
    for (int i = 0; i < ps; i++) dfs(i, 1, p[i], 1);
    return ans;
  }

 private:
  i64 md(i64 n, i64 d) { return double(n) / d; }
  i64 idx(i64 n) { return n <= sq ? s - n : md(M, n); }
  void set_buf(vector<T>& _buf) { swap(buf, _buf); }
};

/**
 * @brief 乗法的関数のprefix sum
 * @docs docs/multiplicative-function/sum-of-multiplicative-function.md
 */

//
using namespace Nyaan;
using mint = LazyMontgomeryModInt<998244353>;
// using mint = LazyMontgomeryModInt<1000000007>;
using vm = vector<mint>;
using vvm = vector<vm>;
Binomial<mint> C;

vector<mint> cmemo(50);
mint f(ll, ll c) { return cmemo[c + 1]; }
void Nyaan::solve() {
  inl(N, M);
  rep(i, 50) cmemo[i] = mint{i}.pow(N);
  mf_prefix_sum<mint, f> mf(M);
  auto pi = mf.pi_table();
  mint coe = mint{2}.pow(N);
  each(x, pi) x *= coe;
  out(mf.run(pi));
}
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