QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#841952#9782. NonZero PrefSuf SumshcywoiAC ✓501ms3884kbC++234.2kb2025-01-04 09:03:082025-01-04 09:03:17

Judging History

你现在查看的是最新测评结果

  • [2025-01-04 09:03:17]
  • 评测
  • 测评结果:AC
  • 用时:501ms
  • 内存:3884kb
  • [2025-01-04 09:03:08]
  • 提交

answer

#include <bits/stdc++.h>

using i64 = long long;

template<class T>
T qmi(T a, i64 b) {
  T res = 1;
  for (; b; b /= 2, a *= a) {
    if (b % 2) {
      res *= a;
    }
  }
  return res;
}

i64 mul(i64 a, i64 b, i64 p) {
  i64 res = a * b - i64(1.L * a * b / p) * p;
  res %= p;
  if (res < 0) {
    res += p;
  }
  return res;
}

template<int P>
struct modint {
  int x;
  constexpr modint() : x{} {}
  constexpr modint(i64 x) : x{norm(x % getmod())} {}

  static int mod;
  constexpr static int getmod() {
    if (P > 0) {
      return P;
    } else {
      return mod;
    }
  }
  constexpr static void setmod(int m) {
    mod = m;
  }
  constexpr int norm(int x) const {
    if (x < 0) {
      x += getmod();
    }
    if (x >= getmod()) {
      x -= getmod();
    }
    return x;
  }
  constexpr int val() const {
    return x;
  }
  explicit constexpr operator int() const {
    return x;
  }
  constexpr modint operator-() const {
    modint res;
    res.x = norm(getmod() - x);
    return res;
  }
  constexpr modint inv() const {
    assert(x != 0);
    return qmi(*this, getmod() - 2);
  }
  constexpr modint &operator*= (modint v) & {
    x = 1LL * x * v.x % getmod();
    return *this;
  }
  constexpr modint &operator+= (modint v) & {
    x = norm(x + v.x);
    return *this;
  }
  constexpr modint &operator-= (modint v) & {
    x = norm(x - v.x);
    return *this;
  }
  constexpr modint &operator/= (modint v) & {
    return *this *= v.inv();
  }
  friend constexpr modint operator- (modint a, modint b) {
    modint res = a;
    res -= b;
    return res;
  }
  friend constexpr modint operator+ (modint a, modint b) {
    modint res = a;
    res += b;
    return res;
  }
  friend constexpr modint operator* (modint a, modint b) {
    modint res = a;
    res *= b;
    return res;
  }
  friend constexpr modint operator/ (modint a, modint b) {
    modint res = a;
    res /= b;
    return res;
  }
  friend constexpr std::istream &operator>> (std::istream& is, modint& a) {
    i64 v;
    is >> v;
    a = modint(v);
    return is;
  }
  friend constexpr std::ostream &operator<< (std::ostream& os, const modint& a) {
    return os << a.val();
  }
  friend constexpr bool operator== (modint a, modint b) {
    return a.val() == b.val();
  }
  friend constexpr bool operator!= (modint a, modint b) {
    return a.val() != b.val();
  }
};

template<>
int modint<0>::mod = 998244353;
using mint = modint<0>;

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);

  int n, m, p;
  std::cin >> n >> m >> p;

  mint::mod = p;

  mint ans = qmi(mint(m * 2 + 1), n);
  {
    std::vector<mint> dp(n * m + 1);
    dp[0] = 1;
    for (int i = 0; i < n; i++) {
      for (int j = 1; j <= n * m; j++) {
        dp[j] += dp[j - 1];
      }
      for (int j = n * m; j >= m * 2 + 1; j--) {
        dp[j] -= dp[j - m * 2 - 1];
      }
    }
    ans -= dp[n * m];
  }

  auto get = [&](int m) {
    mint ans = 0;
    for (int s = 1; s <= n; s++) {
      std::vector<std::array<mint, 2>> dp(n * 2 + 1);
      dp[n][0] = 1;
      for (int i = 0; i < n; i++) {
        std::vector<std::array<mint, 2>> ndp(n * 2 + 1);
        for (int j = 0; j <= n * 2; j++) {
          for (int t = 0; t < 2; t++) {
            int l = std::max(-j, -m);
            int r = std::min(n * 2 - j + 1, 2 - s);
            if (l < r) {
              ndp[j + l][1] += dp[j][t];
              if (j + r <= n * 2) {
                ndp[j + r][1] -= dp[j][t];
              }
            }
            l = std::max({-j, -m, 2 - s});
            r = std::min(n * 2 - j + 1, 2);
            if (l < r) {
              ndp[j + l][t] += dp[j][t];
              if (j + r <= n * 2) {
                ndp[j + r][t] -= dp[j][t];
              }
            }
          }
        }
        for (int j = 1; j <= n * 2; j++) {
          for (int t = 0; t < 2; t++) {
            ndp[j][t] += ndp[j - 1][t];
          }
        }
        dp = std::move(ndp);
      }
      ans += dp[n + s][1];
    }
    return ans;
  };

  for (int l = 1, r; l <= m; l = r + 1) {
    r = m / (m / l);
    ans -= (r - l + 1) * get(m / l) * 2;
  }
  std::cout << ans << "\n";

  return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 0ms
memory: 3580kb

input:

2 1 998244353

output:

2

result:

ok single line: '2'

Test #2:

score: 0
Accepted
time: 133ms
memory: 3588kb

input:

69 42 696969697

output:

378553557

result:

ok single line: '378553557'

Test #3:

score: 0
Accepted
time: 0ms
memory: 3624kb

input:

2 1 998244353

output:

2

result:

ok single line: '2'

Test #4:

score: 0
Accepted
time: 103ms
memory: 3884kb

input:

69 42 696969697

output:

378553557

result:

ok single line: '378553557'

Test #5:

score: 0
Accepted
time: 99ms
memory: 3880kb

input:

61 75 677323601

output:

34613998

result:

ok single line: '34613998'

Test #6:

score: 0
Accepted
time: 1ms
memory: 3512kb

input:

13 14 670577333

output:

41465431

result:

ok single line: '41465431'

Test #7:

score: 0
Accepted
time: 1ms
memory: 3832kb

input:

14 6 987686347

output:

37536510

result:

ok single line: '37536510'

Test #8:

score: 0
Accepted
time: 1ms
memory: 3828kb

input:

15 12 196428923

output:

29322522

result:

ok single line: '29322522'

Test #9:

score: 0
Accepted
time: 31ms
memory: 3664kb

input:

68 7 786815587

output:

149281835

result:

ok single line: '149281835'

Test #10:

score: 0
Accepted
time: 0ms
memory: 3624kb

input:

3 2 503002109

output:

82

result:

ok single line: '82'

Test #11:

score: 0
Accepted
time: 1ms
memory: 3884kb

input:

13 5 756093197

output:

415698676

result:

ok single line: '415698676'

Test #12:

score: 0
Accepted
time: 0ms
memory: 3628kb

input:

2 3 646574611

output:

30

result:

ok single line: '30'

Test #13:

score: 0
Accepted
time: 26ms
memory: 3804kb

input:

39 68 120037189

output:

43217507

result:

ok single line: '43217507'

Test #14:

score: 0
Accepted
time: 1ms
memory: 3620kb

input:

13 4 423132517

output:

360231790

result:

ok single line: '360231790'

Test #15:

score: 0
Accepted
time: 1ms
memory: 3568kb

input:

14 3 309713387

output:

94215386

result:

ok single line: '94215386'

Test #16:

score: 0
Accepted
time: 7ms
memory: 3604kb

input:

24 77 886983941

output:

211636479

result:

ok single line: '211636479'

Test #17:

score: 0
Accepted
time: 0ms
memory: 3628kb

input:

3 3 504388063

output:

270

result:

ok single line: '270'

Test #18:

score: 0
Accepted
time: 0ms
memory: 3624kb

input:

3 1 936205423

output:

8

result:

ok single line: '8'

Test #19:

score: 0
Accepted
time: 0ms
memory: 3572kb

input:

3 3 295983139

output:

270

result:

ok single line: '270'

Test #20:

score: 0
Accepted
time: 1ms
memory: 3832kb

input:

10 15 446169107

output:

149884328

result:

ok single line: '149884328'

Test #21:

score: 0
Accepted
time: 10ms
memory: 3864kb

input:

37 18 833753929

output:

592917251

result:

ok single line: '592917251'

Test #22:

score: 0
Accepted
time: 0ms
memory: 3628kb

input:

11 3 998773403

output:

860630017

result:

ok single line: '860630017'

Test #23:

score: 0
Accepted
time: 0ms
memory: 3608kb

input:

14 85 688036639

output:

347188409

result:

ok single line: '347188409'

Test #24:

score: 0
Accepted
time: 0ms
memory: 3828kb

input:

3 3 844621907

output:

270

result:

ok single line: '270'

Test #25:

score: 0
Accepted
time: 0ms
memory: 3600kb

input:

3 4 204335891

output:

620

result:

ok single line: '620'

Test #26:

score: 0
Accepted
time: 0ms
memory: 3832kb

input:

7 8 113007667

output:

58946097

result:

ok single line: '58946097'

Test #27:

score: 0
Accepted
time: 0ms
memory: 3800kb

input:

4 1 637268377

output:

22

result:

ok single line: '22'

Test #28:

score: 0
Accepted
time: 1ms
memory: 3796kb

input:

11 14 391637237

output:

303270280

result:

ok single line: '303270280'

Test #29:

score: 0
Accepted
time: 0ms
memory: 3568kb

input:

3 2 208286231

output:

82

result:

ok single line: '82'

Test #30:

score: 0
Accepted
time: 0ms
memory: 3572kb

input:

2 11 662696483

output:

462

result:

ok single line: '462'

Test #31:

score: 0
Accepted
time: 3ms
memory: 3576kb

input:

19 55 974135299

output:

887460557

result:

ok single line: '887460557'

Test #32:

score: 0
Accepted
time: 0ms
memory: 3596kb

input:

6 8 417027509

output:

23351024

result:

ok single line: '23351024'

Test #33:

score: 0
Accepted
time: 1ms
memory: 3808kb

input:

8 13 624006587

output:

353008442

result:

ok single line: '353008442'

Test #34:

score: 0
Accepted
time: 1ms
memory: 3792kb

input:

10 10 740294671

output:

79436611

result:

ok single line: '79436611'

Test #35:

score: 0
Accepted
time: 1ms
memory: 3572kb

input:

11 10 394088657

output:

161476458

result:

ok single line: '161476458'

Test #36:

score: 0
Accepted
time: 1ms
memory: 3872kb

input:

9 27 562853573

output:

135252259

result:

ok single line: '135252259'

Test #37:

score: 0
Accepted
time: 0ms
memory: 3572kb

input:

8 3 829129009

output:

5349034

result:

ok single line: '5349034'

Test #38:

score: 0
Accepted
time: 47ms
memory: 3524kb

input:

51 49 924010279

output:

815049368

result:

ok single line: '815049368'

Test #39:

score: 0
Accepted
time: 0ms
memory: 3864kb

input:

12 2 308466749

output:

223013998

result:

ok single line: '223013998'

Test #40:

score: 0
Accepted
time: 0ms
memory: 3664kb

input:

7 4 567557693

output:

4502296

result:

ok single line: '4502296'

Test #41:

score: 0
Accepted
time: 25ms
memory: 3576kb

input:

36 93 943780729

output:

13599465

result:

ok single line: '13599465'

Test #42:

score: 0
Accepted
time: 0ms
memory: 3860kb

input:

2 1 828681127

output:

2

result:

ok single line: '2'

Test #43:

score: 0
Accepted
time: 0ms
memory: 3532kb

input:

3 3 534160729

output:

270

result:

ok single line: '270'

Test #44:

score: 0
Accepted
time: 1ms
memory: 3864kb

input:

7 12 920925433

output:

453086694

result:

ok single line: '453086694'

Test #45:

score: 0
Accepted
time: 0ms
memory: 3628kb

input:

3 2 440546987

output:

82

result:

ok single line: '82'

Test #46:

score: 0
Accepted
time: 85ms
memory: 3564kb

input:

90 9 291269963

output:

72560304

result:

ok single line: '72560304'

Test #47:

score: 0
Accepted
time: 4ms
memory: 3568kb

input:

38 10 867575113

output:

165530481

result:

ok single line: '165530481'

Test #48:

score: 0
Accepted
time: 33ms
memory: 3796kb

input:

48 37 152663531

output:

135425620

result:

ok single line: '135425620'

Test #49:

score: 0
Accepted
time: 1ms
memory: 3632kb

input:

15 15 991731803

output:

102703562

result:

ok single line: '102703562'

Test #50:

score: 0
Accepted
time: 501ms
memory: 3612kb

input:

100 100 696969697

output:

313377809

result:

ok single line: '313377809'

Extra Test:

score: 0
Extra Test Passed