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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#260370#7838. 往日之影hos_lyric#40 127ms15668kbC++147.6kb2023-11-22 04:52:212024-07-04 03:08:06

Judging History

你现在查看的是最新测评结果

  • [2024-07-04 03:08:06]
  • 评测
  • 测评结果:40
  • 用时:127ms
  • 内存:15668kb
  • [2023-11-22 04:52:21]
  • 提交

answer

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
// Barrett
struct ModInt {
  static unsigned M;
  static unsigned long long NEG_INV_M;
  static void setM(unsigned m) { M = m; NEG_INV_M = -1ULL / M; }
  unsigned x;
  ModInt() : x(0U) {}
  ModInt(unsigned x_) : x(x_ % M) {}
  ModInt(unsigned long long x_) : x(x_ % M) {}
  ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) {
    const unsigned long long y = static_cast<unsigned long long>(x) * a.x;
    const unsigned long long q = static_cast<unsigned long long>((static_cast<unsigned __int128>(NEG_INV_M) * y) >> 64);
    const unsigned long long r = y - M * q;
    x = r - M * (r >= M);
    return *this;
  }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
unsigned ModInt::M;
unsigned long long ModInt::NEG_INV_M;
// !!!Use ModInt::setM!!!
////////////////////////////////////////////////////////////////////////////////

using Mint = ModInt;

constexpr int LIM_INV = 1'000'010;
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];

void prepare() {
  inv[1] = 1;
  for (int i = 2; i < LIM_INV; ++i) {
    inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
  }
  fac[0] = invFac[0] = 1;
  for (int i = 1; i < LIM_INV; ++i) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(Int n, Int k) {
  if (n < 0) {
    if (k >= 0) {
      return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
    } else if (n - k >= 0) {
      return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
    } else {
      return 0;
    }
  } else {
    if (0 <= k && k <= n) {
      assert(n < LIM_INV);
      return fac[n] * invFac[k] * invFac[n - k];
    } else {
      return 0;
    }
  }
}


struct F {
  Mint x, y;
  F(Mint x_ = 0, Mint y_ = 0) : x(x_), y(y_) {}
  friend ostream &operator<<(ostream &os, const F &f) {
    if (!f.y) return os << f.x;
    if (!f.x) return os << f.y << "i";
    return os << f.x << "+" << f.y << "i";
  }
  F operator+(const F &f) const { return F(x + f.x, y + f.y); }
  F operator*(const F &f) const { return F(x * f.x - y * f.y, x * f.y + y * f.x); }
  F operator*(const Mint &a) const { return F(x * a, y * a); }
};

int main() {
  int MO;
  for (int numCases; ~scanf("%d%d", &numCases, &MO); ) { for (int caseId = 1; caseId <= numCases; ++caseId) {
    Mint::setM(MO);
    prepare();
    const F I[4] = {F(1, 0), F(0, 1), F(-1, 0), F(0, -1)};
    
    int N, A[4];
    scanf("%d", &N);
    for (int j = 0; j < 4; ++j) {
      scanf("%d", &A[j]);
    }
    
    /*
      i^1: at most 1
      i^3: at most 1
      i^0, i^2: not both
    */
    F ans;
    for (const int s : {0, 2}) {
      int base = 0;
      for (int j = 0; j < 4; ++j) {
        base -= A[j] * (s * j);
      }
      base &= 3;
      if (N >= (s ? 1 : 0)) {
        // 2^binom(N,2)
        const F f = I[base] * Mint(2).pow((Int)N*(N-1)/2);
// cerr<<"s="<<s<<" "<<__LINE__<<"> "<<f<<endl;
        ans = ans + f;
      }
      if (N - 1 >= (s ? 1 : 0)) {
        F f;
        for (int j1 = 0; j1 < 4; ++j1) if (A[j1]) {
          f = f + I[(base - 1 * j1) & 3] * A[j1];
        }
        // 2^binom(N-1,2) (1+i)^(N-1)
        f = f * Mint(2).pow((Int)(N-1)*(N-2)/2 + (N-1)/2) * I[((N-1)/2) & 3];
        if ((N-1) & 1) {
          f = f * F(1, 1);
        }
// cerr<<"s="<<s<<" "<<__LINE__<<"> "<<f<<endl;
        ans = ans + f;
      }
      if (N - 1 >= (s ? 1 : 0)) {
        F f;
        for (int j3 = 0; j3 < 4; ++j3) if (A[j3]) {
          f = f + I[(base - 3 * j3) & 3] * A[j3];
        }
        // 2^binom(N-1,2) (1-i)^(N-1)
        f = f * Mint(2).pow((Int)(N-1)*(N-2)/2 + (N-1)/2) * I[(-((N-1)/2)) & 3];
        if ((N-1) & 1) {
          f = f * F(1, -1);
        }
// cerr<<"s="<<s<<" "<<__LINE__<<"> "<<f<<endl;
        ans = ans + f;
      }
      if (N - 2 >= (s ? 1 : 0)) {
        F f;
        for (int j1 = 0; j1 < 4; ++j1) if (A[j1]) {
          const Mint a = A[j1];
          --A[j1];
          for (int j3 = 0; j3 < 4; ++j3) if (A[j3]) {
            const Mint aa = a * A[j3];
            f = f + I[(base - 1 * j1 - 3 * j3) & 3] * aa;
          }
          ++A[j1];
        }
        // 2^binom(N-2,2) (1+i)^(N-2) (1-i)^(N-2) 2^1
        f = f * Mint(2).pow((Int)(N-2)*(N-3)/2 + (N-2) + 1);
// cerr<<"s="<<s<<" "<<__LINE__<<"> "<<f<<endl;
        ans = ans + f;
      }
    }
    ans = ans * Mint(4).pow(-N);
// cerr<<"ans = "<<ans<<endl;
    ans = ans * Mint(2).pow(-(Int)N*(N-1)/2);
    printf("%u\n", ans.x.x);
  }
#ifndef LOCAL
  break;
#endif
  }
  return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Subtask #1:

score: 10
Accepted

Test #1:

score: 10
Accepted
time: 8ms
memory: 15528kb

input:

1 998244353
3
1 1 0 1

output:

0

result:

ok single line: '0'

Test #2:

score: 0
Accepted
time: 12ms
memory: 15584kb

input:

1 998244353
7
0 2 1 4

output:

998069185

result:

ok single line: '998069185'

Test #3:

score: 0
Accepted
time: 8ms
memory: 15580kb

input:

1 998244353
4
0 1 0 3

output:

0

result:

ok single line: '0'

Test #4:

score: 0
Accepted
time: 11ms
memory: 15508kb

input:

1 998244353
2
1 0 1 0

output:

0

result:

ok single line: '0'

Test #5:

score: 0
Accepted
time: 8ms
memory: 15480kb

input:

1 998244353
6
2 1 0 3

output:

997696001

result:

ok single line: '997696001'

Test #6:

score: 0
Accepted
time: 7ms
memory: 15508kb

input:

1 998244353
2
1 0 1 0

output:

0

result:

ok single line: '0'

Subtask #2:

score: 20
Accepted

Dependency #1:

100%
Accepted

Test #7:

score: 20
Accepted
time: 8ms
memory: 15476kb

input:

1 998244353
40
11 9 9 11

output:

855684614

result:

ok single line: '855684614'

Test #8:

score: 0
Accepted
time: 7ms
memory: 15588kb

input:

1 998244353
39
12 8 7 12

output:

629648158

result:

ok single line: '629648158'

Test #9:

score: 0
Accepted
time: 8ms
memory: 15592kb

input:

1 998244353
38
13 8 9 8

output:

944107686

result:

ok single line: '944107686'

Test #10:

score: 0
Accepted
time: 8ms
memory: 15608kb

input:

1 998244353
37
16 7 7 7

output:

393700837

result:

ok single line: '393700837'

Test #11:

score: 0
Accepted
time: 38ms
memory: 15592kb

input:

4 998244353
10
0 3 2 5
9
2 1 1 5
10
1 2 3 4
9
4 0 3 2

output:

124779131
998235309
124779131
998236023

result:

ok 4 lines

Test #12:

score: 0
Accepted
time: 35ms
memory: 15604kb

input:

4 998244353
10
2 1 4 3
9
1 2 4 2
10
3 2 5 0
9
3 2 2 2

output:

124779131
998239593
124778655
998236261

result:

ok 4 lines

Test #13:

score: 0
Accepted
time: 33ms
memory: 15612kb

input:

4 998244353
10
1 4 1 4
9
2 0 5 2
10
3 5 1 1
9
6 1 1 1

output:

623900891
998239355
374338940
998231025

result:

ok 4 lines

Test #14:

score: 0
Accepted
time: 69ms
memory: 15668kb

input:

8 998244353
4
2 1 0 1
4
0 2 0 2
5
0 1 1 3
4
0 1 0 3
5
1 1 0 3
5
0 3 1 1
4
2 2 0 0
5
1 1 2 1

output:

0
0
995319809
0
997269505
995319809
982646785
996294657

result:

ok 8 lines

Test #15:

score: 0
Accepted
time: 72ms
memory: 15584kb

input:

8 998244353
4
2 1 0 1
4
3 0 1 0
4
0 2 2 0
5
2 0 1 2
5
1 2 0 2
5
0 1 1 3
5
0 1 1 3
4
1 1 1 1

output:

0
0
967049217
997269505
0
995319809
995319809
0

result:

ok 8 lines

Test #16:

score: 0
Accepted
time: 30ms
memory: 15612kb

input:

3 998244353
30
1 10 7 12
8
0 3 0 5
2
0 1 0 1

output:

54137262
998208177
0

result:

ok 3 lines

Subtask #3:

score: 10
Accepted

Dependency #2:

100%
Accepted

Test #17:

score: 10
Accepted
time: 8ms
memory: 15532kb

input:

1 998244353
99
12 22 33 32
15 998244353
7
1 2 2 2
6
1 2 1 2
6
1 1 3 1
7
0 3 1 3
7
1 1 2 3
7
3 1 0 3
6
1 2 1 2
7
1 2 2 2
7
3 3 0 1
6
1 1 3 1
7
5 1 0 1
6
3 0 1 2
6
2 0 0 4
7
2 0 1 4
6
4 1 0 1

output:

940435798

result:

ok single line: '940435798'

Test #18:

score: 0
Accepted
time: 8ms
memory: 15600kb

input:

1 998244353
98
27 29 23 19
15 998244353
7
2 2 1 2
6
0 1 2 3
6
0 2 2 2
6
6 0 0 0
7
4 1 1 1
7
2 1 1 3
7
2 1 1 3
7
2 3 1 1
7
3 3 0 1
6
3 1 1 1
6
3 1 1 1
7
2 1 1 3
6
1 1 3 1
6
1 1 3 1
6
2 0 4 0

output:

147819391

result:

ok single line: '147819391'

Test #19:

score: 0
Accepted
time: 26ms
memory: 15480kb

input:

3 998244353
70
15 17 13 25
20
8 3 4 5
10
3 2 5 0
15 998244353
7
5 1 0 1
6
0 1 4 1
7
1 3 2 1
6
1 0 1 4
7
2 2 1 2
7
2 1 1 3
7
2 3 1 1
6
6 0 0 0
6
3 2 1 0
7
2 3 1 1
7
1 1 2 3
6
2 1 2 1
6
1 2 1 2
6
1 1 1 3
7
2 2 3 0

output:

300715311
500913543
124778655

result:

ok 3 lines

Test #20:

score: 0
Accepted
time: 25ms
memory: 15592kb

input:

3 998244353
70
21 23 11 15
20
5 4 3 8
10
5 1 1 3
15 998244353
6
1 0 3 2
7
3 1 0 3
6
2 2 0 2
7
1 3 0 3
7
2 2 3 0
6
3 0 3 0
6
1 0 3 2
7
1 1 2 3
6
1 1 1 3
7
1 2 0 4
7
2 1 1 3
6
4 0 0 2
6
2 2 2 0
6
2 2 0 2
6
0 1 2 3

output:

367385542
500913543
374339416

result:

ok 3 lines

Test #21:

score: 0
Accepted
time: 90ms
memory: 15520kb

input:

10 998244353
9
2 4 1 2
10
3 4 1 2
10
1 2 3 4
10
2 3 4 1
10
3 1 3 3
9
0 4 3 2
9
2 3 1 3
10
4 2 2 2
9
4 1 1 3
9
2 3 1 3
15 998244353
7
1 3 0 3
6
3 2 1 0
6
0 2 0 4
6
0 4 2 0
7
1 3 0 3
6
1 1 3 1
6
1 4 1 0
7
1 1 2 3
6
2 3 0 1
7
3 1 2 1
6
4 0 2 0
6
2 2 2 0
6
2 1 2 1
7
3 2 2 0
6
0 0 4 2

output:

998236023
124778179
124779131
124778655
374340011
998239355
998236261
374339535
998233643
998236261

result:

ok 10 lines

Test #22:

score: 0
Accepted
time: 127ms
memory: 15476kb

input:

15 998244353
7
3 2 2 0
7
2 2 3 0
6
1 3 1 1
7
1 1 2 3
6
1 3 1 1
7
3 3 0 1
6
2 1 2 1
6
1 2 1 2
6
1 1 1 3
6
4 1 0 1
7
3 2 2 0
6
1 3 1 1
6
0 2 2 2
7
1 3 0 3
7
2 2 1 2

output:

998191041
998191041
998061569
998069185
998061569
998160577
997939713
997939713
997574145
997939713
998191041
998061569
997574145
998145345
998145345

result:

ok 15 lines

Subtask #4:

score: 0
Time Limit Exceeded

Test #23:

score: 0
Time Limit Exceeded

input:

999 999999001
2
2 0 0 0
3
3 0 0 0
4
4 0 0 0
5
5 0 0 0
6
6 0 0 0
7
7 0 0 0
8
8 0 0 0
9
9 0 0 0
10
10 0 0 0
11
11 0 0 0
12
12 0 0 0
13
13 0 0 0
14
14 0 0 0
15
15 0 0 0
16
16 0 0 0
17
17 0 0 0
18
18 0 0 0
19
19 0 0 0
20
20 0 0 0
21
21 0 0 0
22
22 0 0 0
23
23 0 0 0
24
24 0 0 0
25
25 0 0 0
26
26 0 0 0
27...

output:


result:


Subtask #5:

score: 0
Skipped

Dependency #1:

100%
Accepted

Dependency #2:

100%
Accepted

Dependency #3:

100%
Accepted

Dependency #4:

0%