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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#884431#9782. NonZero PrefSuf SumsfxhdAC ✓132ms3840kbC++1416.4kb2025-02-06 07:45:002025-02-06 07:45:01

Judging History

This is the latest submission verdict.

  • [2025-02-06 07:45:01]
  • Judged
  • Verdict: AC
  • Time: 132ms
  • Memory: 3840kb
  • [2025-02-06 07:45:00]
  • Submitted

answer

#include <bits/stdc++.h>

#include <cassert>
#include <numeric>
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif


#include <utility>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

struct barrett {
    unsigned int _m;
    unsigned long long im;

    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    unsigned int umod() const { return _m; }

    unsigned int mul(unsigned int a, unsigned int b) const {

        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 long long y = x * _m;
        return (unsigned int)(z - y + (z < y ? _m : 0));
    }
};

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;
}

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);

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};

    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


        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

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);

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;
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder


#include <cassert>
#include <numeric>
#include <type_traits>

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


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


using namespace std;

#ifdef DEBUG
  #include "debug.hpp"
#else
  #define dbg(...) 0
#endif

using mint = atcoder::modint;

vector<mint> factorial, invfact;

void make_factorials(int max_n) {
  factorial.assign(max_n + 1, 1);
  invfact.resize(max_n + 1);
  for (int i = 1; i <= max_n; ++i) {
    factorial[i] = factorial[i - 1] * i;
  }
  invfact[max_n] = factorial[max_n].inv();
  for (int i = max_n - 1; i >= 0; --i) {
    invfact[i] = invfact[i + 1] * (i + 1);
  }
}

mint choose(int n, int k) {
  if ((n < k) || (k < 0)) return 0;
  return factorial[n] * invfact[k] * invfact[n - k];
}

int solve(int n, int m) {
  make_factorials(n);
  mint ans = 0;
  vector<vector<mint>> dp(n + 1, vector<mint>(n + 1, 0));
  for (int i = 1; i < n; ++i) {
    for (int j = 0; (i + j) < n; ++j) {
      dp[i + j][i] = invfact[i] * invfact[j];
    }
  }
  vector<mint> dp0(2 * n * m + 1, 0);
  dp0[n * m] = 1;
  for (int i = 0; i < n; ++i) {
    vector<mint> ndp(2 * n * m + 1, 0);
    for (int x = -m; x <= m; ++x) {
      for (int s = -i * m; s <= i * m; ++s) {
        ndp[s + x + n * m] += dp0[s + n * m];
      }
    }
    ndp.swap(dp0);
  }
  for (int x = 1; x <= m; ++x) {
    vector<vector<mint>> ndp = dp;
    for (int i = 1; i <= n; ++i) {
      for (int s = 1; s <= n; ++s) {
        for (int j = 1; ((j + i) <= n) && (s - j * x > 0); ++j) {
          int s2 = s - j * x;
          if (((i + j) == n) && (x + 1 >= s2)) {
            ans += dp[i][s] * invfact[j] * mint(m / x) * 2;
          }
          ndp[i + j][s2] += dp[i][s] * invfact[j];
        }
      }
    }
    ndp.swap(dp);
  }
  ans *= factorial[n];
  ans += dp0[n * m];
  if (n > 1) ans += n * mint(2 * m);
  return (mint(2 * m + 1).pow(n) - ans).val();
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, m, p;
  cin >> n >> m >> p;
  mint::set_mod(p);
  cout << solve(n, m) << '\n';
}

詳細信息

Test #1:

score: 100
Accepted
time: 1ms
memory: 3584kb

input:

2 1 998244353

output:

2

result:

ok single line: '2'

Test #2:

score: 0
Accepted
time: 11ms
memory: 3712kb

input:

69 42 696969697

output:

378553557

result:

ok single line: '378553557'

Test #3:

score: 0
Accepted
time: 0ms
memory: 3584kb

input:

2 1 998244353

output:

2

result:

ok single line: '2'

Test #4:

score: 0
Accepted
time: 13ms
memory: 3712kb

input:

69 42 696969697

output:

378553557

result:

ok single line: '378553557'

Test #5:

score: 0
Accepted
time: 28ms
memory: 3584kb

input:

61 75 677323601

output:

34613998

result:

ok single line: '34613998'

Test #6:

score: 0
Accepted
time: 1ms
memory: 3584kb

input:

13 14 670577333

output:

41465431

result:

ok single line: '41465431'

Test #7:

score: 0
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time: 1ms
memory: 3584kb

input:

14 6 987686347

output:

37536510

result:

ok single line: '37536510'

Test #8:

score: 0
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time: 1ms
memory: 3712kb

input:

15 12 196428923

output:

29322522

result:

ok single line: '29322522'

Test #9:

score: 0
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time: 1ms
memory: 3840kb

input:

68 7 786815587

output:

149281835

result:

ok single line: '149281835'

Test #10:

score: 0
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time: 0ms
memory: 3712kb

input:

3 2 503002109

output:

82

result:

ok single line: '82'

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score: 0
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time: 0ms
memory: 3712kb

input:

13 5 756093197

output:

415698676

result:

ok single line: '415698676'

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score: 0
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time: 0ms
memory: 3584kb

input:

2 3 646574611

output:

30

result:

ok single line: '30'

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score: 0
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time: 9ms
memory: 3584kb

input:

39 68 120037189

output:

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result:

ok single line: '43217507'

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score: 0
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time: 0ms
memory: 3584kb

input:

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output:

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ok single line: '360231790'

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score: 0
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time: 0ms
memory: 3584kb

input:

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output:

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result:

ok single line: '94215386'

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score: 0
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time: 4ms
memory: 3840kb

input:

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output:

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result:

ok single line: '211636479'

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score: 0
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time: 0ms
memory: 3584kb

input:

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output:

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ok single line: '270'

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score: 0
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time: 0ms
memory: 3584kb

input:

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output:

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ok single line: '8'

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score: 0
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time: 0ms
memory: 3584kb

input:

3 3 295983139

output:

270

result:

ok single line: '270'

Test #20:

score: 0
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time: 1ms
memory: 3712kb

input:

10 15 446169107

output:

149884328

result:

ok single line: '149884328'

Test #21:

score: 0
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time: 1ms
memory: 3584kb

input:

37 18 833753929

output:

592917251

result:

ok single line: '592917251'

Test #22:

score: 0
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time: 0ms
memory: 3584kb

input:

11 3 998773403

output:

860630017

result:

ok single line: '860630017'

Test #23:

score: 0
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time: 2ms
memory: 3712kb

input:

14 85 688036639

output:

347188409

result:

ok single line: '347188409'

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score: 0
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time: 0ms
memory: 3712kb

input:

3 3 844621907

output:

270

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ok single line: '270'

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score: 0
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memory: 3712kb

input:

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output:

620

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ok single line: '620'

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score: 0
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time: 0ms
memory: 3584kb

input:

7 8 113007667

output:

58946097

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ok single line: '58946097'

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score: 0
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time: 0ms
memory: 3712kb

input:

4 1 637268377

output:

22

result:

ok single line: '22'

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score: 0
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time: 0ms
memory: 3712kb

input:

11 14 391637237

output:

303270280

result:

ok single line: '303270280'

Test #29:

score: 0
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time: 0ms
memory: 3584kb

input:

3 2 208286231

output:

82

result:

ok single line: '82'

Test #30:

score: 0
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time: 0ms
memory: 3584kb

input:

2 11 662696483

output:

462

result:

ok single line: '462'

Test #31:

score: 0
Accepted
time: 1ms
memory: 3584kb

input:

19 55 974135299

output:

887460557

result:

ok single line: '887460557'

Test #32:

score: 0
Accepted
time: 0ms
memory: 3584kb

input:

6 8 417027509

output:

23351024

result:

ok single line: '23351024'

Test #33:

score: 0
Accepted
time: 0ms
memory: 3712kb

input:

8 13 624006587

output:

353008442

result:

ok single line: '353008442'

Test #34:

score: 0
Accepted
time: 1ms
memory: 3712kb

input:

10 10 740294671

output:

79436611

result:

ok single line: '79436611'

Test #35:

score: 0
Accepted
time: 0ms
memory: 3712kb

input:

11 10 394088657

output:

161476458

result:

ok single line: '161476458'

Test #36:

score: 0
Accepted
time: 1ms
memory: 3712kb

input:

9 27 562853573

output:

135252259

result:

ok single line: '135252259'

Test #37:

score: 0
Accepted
time: 0ms
memory: 3584kb

input:

8 3 829129009

output:

5349034

result:

ok single line: '5349034'

Test #38:

score: 0
Accepted
time: 7ms
memory: 3840kb

input:

51 49 924010279

output:

815049368

result:

ok single line: '815049368'

Test #39:

score: 0
Accepted
time: 1ms
memory: 3584kb

input:

12 2 308466749

output:

223013998

result:

ok single line: '223013998'

Test #40:

score: 0
Accepted
time: 0ms
memory: 3712kb

input:

7 4 567557693

output:

4502296

result:

ok single line: '4502296'

Test #41:

score: 0
Accepted
time: 15ms
memory: 3712kb

input:

36 93 943780729

output:

13599465

result:

ok single line: '13599465'

Test #42:

score: 0
Accepted
time: 0ms
memory: 3584kb

input:

2 1 828681127

output:

2

result:

ok single line: '2'

Test #43:

score: 0
Accepted
time: 0ms
memory: 3712kb

input:

3 3 534160729

output:

270

result:

ok single line: '270'

Test #44:

score: 0
Accepted
time: 0ms
memory: 3712kb

input:

7 12 920925433

output:

453086694

result:

ok single line: '453086694'

Test #45:

score: 0
Accepted
time: 0ms
memory: 3712kb

input:

3 2 440546987

output:

82

result:

ok single line: '82'

Test #46:

score: 0
Accepted
time: 3ms
memory: 3712kb

input:

90 9 291269963

output:

72560304

result:

ok single line: '72560304'

Test #47:

score: 0
Accepted
time: 1ms
memory: 3712kb

input:

38 10 867575113

output:

165530481

result:

ok single line: '165530481'

Test #48:

score: 0
Accepted
time: 6ms
memory: 3840kb

input:

48 37 152663531

output:

135425620

result:

ok single line: '135425620'

Test #49:

score: 0
Accepted
time: 0ms
memory: 3584kb

input:

15 15 991731803

output:

102703562

result:

ok single line: '102703562'

Test #50:

score: 0
Accepted
time: 132ms
memory: 3840kb

input:

100 100 696969697

output:

313377809

result:

ok single line: '313377809'

Extra Test:

score: 0
Extra Test Passed