oj.uz

Submission #890581

# Submission time Handle Problem Language Result Execution time Memory
890581 2023-12-21T13:51:06 Z fanwen NoM (RMI21_nom) C++17
100 / 100
 41 ms 1264 KB 
#include <bits/stdc++.h>

using namespace std;

#define fi first
#define se second
#define ll long long
#define file(name)                  \
    if(fopen(name".inp", "r"))      \
        freopen(name".inp", "r", stdin), freopen(name".out", "w", stdout); 

template <int Mod> 
struct Modular {
private :
    int val;
    static int inverse(int a, int b) {
        a %= b;
        assert(a);
        if(a == 1) return 1;
        return int(b - (long long) inverse(b, a) * (long long) b / a);
    }
public :
    Modular(long long x = 0) : val(x % Mod) { if(val < 0) val += Mod; }

    friend bool operator == (const Modular &a, const Modular &b) { return a.val == b.val; }
    friend bool operator != (const Modular &a, const Modular &b) { return a.val != b.val; }

    Modular& operator = (const long long &x) { val = x % Mod; if(val < 0) val += Mod; return *this; }
    Modular& operator = (const Modular &x) { val = x.val; return *this; }

    friend istream & operator >> (istream &in, Modular &a) { long long x; in >> x; a = Modular(x); return in; }
    friend ostream & operator << (ostream &out, const Modular &a) { return out << a.val; }

    explicit operator int() const { return val; }
    explicit operator bool() const { return val > 0; }

    Modular inv() const {
        Modular res;
        res.val = inverse(val, Mod);
        return res;
    }

    Modular operator ++() { (*this) += 1; return *this; }
    Modular operator --() { (*this) -= 1; return *this; }
    Modular operator ++(int) { (*this) += 1; return *this - 1; }
    Modular operator --(int) { (*this) -= 1; return *this + 1; }

    Modular operator + () const { return *this; }
    Modular operator - () const {
        Modular res;
        res.val = (val ? Mod - val : 0);
        return res;
    }

    Modular& operator += (const Modular &a) {
        val += a.val;
        if(val >= Mod) val -= Mod;
        return *this;
    }
    Modular& operator -= (const Modular &a) {
        val -= a.val;
        if(val < 0) val += Mod;
        return *this;
    }
    Modular& operator *= (const Modular &a) {
        val = 1LL * val * a.val % Mod;
        return *this;
    }
    Modular& operator /= (const Modular &a) {
        (*this) *= a.inv();
        return *this;
    }
    friend Modular operator + (const Modular &a, const Modular &b) { return Modular(a) += b; }
    friend Modular operator - (const Modular &a, const Modular &b) { return Modular(a) -= b; }
    friend Modular operator * (const Modular &a, const Modular &b) { return Modular(a) *= b; }
    friend Modular operator / (const Modular &a, const Modular &b) { return Modular(a) /= b; }
};

// const int Mod = 998244353;
// const int Mod = 1e9 + 9; // 1000000009 
const int Mod = 1e9 + 7; // 1000000007

using Modint = Modular <Mod>;

template <class T> T pow(T a, long long b) {
    T ans = 1, mul = a;
    for (; b; b >>= 1) {
        if(b & 1LL) ans *= mul;
        mul *= mul;
    }
    return ans;
}

const int Max_size = 1e5 + 5;
Modint fact[Max_size + 5], invs[Max_size + 5];

void prepare_Comb() {
    fact[0] = invs[0] = 1;
    for (int i = 1; i <= Max_size; ++i) fact[i] = fact[i - 1] * i;
    invs[Max_size] = fact[Max_size].inv();
    for (int i = Max_size - 1; i >= 1; --i) invs[i] = invs[i + 1] * (i + 1);
}

Modint C(int n, int k) {
    if(n < k || k < 0) return 0;
    return fact[n] * invs[k] * invs[n - k];
}

Modint A(int n, int k) {
    if(n < k || k < 0) return 0;
    return fact[n] * invs[n - k];
}

const int MAX = 2e3 + 5;

int N, M, f[MAX];
Modint dp[2 * MAX];

void you_make_it(void) {
	cin >> N >> M;
	for (int i = 1; i <= 2 * N; ++i) f[i % M]++;
	dp[0] = 1;
	for (int i = 0; i < M; ++i) {
		// int len = (2 * N - i) / M;
		// assert(len == f[i]);
		for (int s = N; s >= 1; --s) {
			for (int j = 1; 2 * j <= f[i] && j <= s; ++j) {
				dp[s] += dp[s - j] * A(f[i], 2 * j) * C(s, j);
			}
		}
	}
	// for (int i = 0; i <= N; ++i) cout << dp[i] << " "; cout << '\n';

	Modint ans = 0;
	for (int i = 0; i <= N; ++i) ans += dp[i] * (i & 1 ? - 1 : 1) * fact[2 * N - 2 * i] * C(N, i);
	cout << ans;
}

signed main() {

#ifdef LOCAL
    freopen("TASK.inp", "r", stdin);
    freopen("TASK.out", "w", stdout);
#endif
    file("nom");
    auto start_time = chrono::steady_clock::now();

    cin.tie(0), cout.tie(0) -> sync_with_stdio(0);

    prepare_Comb();

    you_make_it();

    auto end_time = chrono::steady_clock::now();

    cerr << "\nExecution time : " << chrono::duration_cast <chrono::milliseconds> (end_time - start_time).count() << "[ms]" << endl;

    return (0 ^ 0);
}

// Dream it. Wish it. Do it.

Compilation message

Main.cpp: In function 'int main()':
Main.cpp:10:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   10 |         freopen(name".inp", "r", stdin), freopen(name".out", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
Main.cpp:145:5: note: in expansion of macro 'file'
  145 |     file("nom");
      |     ^~~~
Main.cpp:10:49: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   10 |         freopen(name".inp", "r", stdin), freopen(name".out", "w", stdout);
      |                                          ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
Main.cpp:145:5: note: in expansion of macro 'file'
  145 |     file("nom");
      |     ^~~~

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1116 KB Output is correct
2 Correct 2 ms 1116 KB Output is correct
3 Correct 2 ms 1116 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 2 ms 1116 KB Output is correct
6 Correct 2 ms 1116 KB Output is correct
7 Correct 2 ms 1116 KB Output is correct
8 Correct 2 ms 1116 KB Output is correct
9 Correct 2 ms 1116 KB Output is correct
10 Correct 2 ms 1264 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1116 KB Output is correct
2 Correct 2 ms 1116 KB Output is correct
3 Correct 2 ms 1116 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 2 ms 1116 KB Output is correct
6 Correct 2 ms 1116 KB Output is correct
7 Correct 2 ms 1116 KB Output is correct
8 Correct 2 ms 1116 KB Output is correct
9 Correct 2 ms 1116 KB Output is correct
10 Correct 2 ms 1264 KB Output is correct
11 Correct 2 ms 1116 KB Output is correct
12 Correct 2 ms 1116 KB Output is correct
13 Correct 2 ms 1116 KB Output is correct
14 Correct 2 ms 1196 KB Output is correct
15 Correct 2 ms 1116 KB Output is correct
16 Correct 2 ms 1116 KB Output is correct
17 Correct 2 ms 1116 KB Output is correct
18 Correct 2 ms 1116 KB Output is correct
19 Correct 2 ms 1260 KB Output is correct

Subtask #3
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1116 KB Output is correct
2 Correct 2 ms 1116 KB Output is correct
3 Correct 2 ms 1116 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 2 ms 1116 KB Output is correct
6 Correct 2 ms 1116 KB Output is correct
7 Correct 2 ms 1116 KB Output is correct
8 Correct 2 ms 1116 KB Output is correct
9 Correct 2 ms 1116 KB Output is correct
10 Correct 2 ms 1264 KB Output is correct
11 Correct 2 ms 1116 KB Output is correct
12 Correct 2 ms 1116 KB Output is correct
13 Correct 2 ms 1116 KB Output is correct
14 Correct 2 ms 1196 KB Output is correct
15 Correct 2 ms 1116 KB Output is correct
16 Correct 2 ms 1116 KB Output is correct
17 Correct 2 ms 1116 KB Output is correct
18 Correct 2 ms 1116 KB Output is correct
19 Correct 2 ms 1260 KB Output is correct
20 Correct 2 ms 1116 KB Output is correct
21 Correct 2 ms 1112 KB Output is correct
22 Correct 3 ms 1116 KB Output is correct
23 Correct 2 ms 1256 KB Output is correct
24 Correct 3 ms 1116 KB Output is correct
25 Correct 3 ms 1264 KB Output is correct
26 Correct 2 ms 1116 KB Output is correct
27 Correct 3 ms 1116 KB Output is correct

Subtask #4
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1116 KB Output is correct
2 Correct 2 ms 1116 KB Output is correct
3 Correct 2 ms 1116 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 2 ms 1116 KB Output is correct
6 Correct 2 ms 1116 KB Output is correct
7 Correct 2 ms 1116 KB Output is correct
8 Correct 2 ms 1116 KB Output is correct
9 Correct 2 ms 1116 KB Output is correct
10 Correct 2 ms 1264 KB Output is correct
11 Correct 2 ms 1116 KB Output is correct
12 Correct 2 ms 1116 KB Output is correct
13 Correct 2 ms 1116 KB Output is correct
14 Correct 2 ms 1196 KB Output is correct
15 Correct 2 ms 1116 KB Output is correct
16 Correct 2 ms 1116 KB Output is correct
17 Correct 2 ms 1116 KB Output is correct
18 Correct 2 ms 1116 KB Output is correct
19 Correct 2 ms 1260 KB Output is correct
20 Correct 2 ms 1116 KB Output is correct
21 Correct 2 ms 1112 KB Output is correct
22 Correct 3 ms 1116 KB Output is correct
23 Correct 2 ms 1256 KB Output is correct
24 Correct 3 ms 1116 KB Output is correct
25 Correct 3 ms 1264 KB Output is correct
26 Correct 2 ms 1116 KB Output is correct
27 Correct 3 ms 1116 KB Output is correct
28 Correct 5 ms 1112 KB Output is correct
29 Correct 6 ms 1116 KB Output is correct
30 Correct 6 ms 1260 KB Output is correct
31 Correct 5 ms 1116 KB Output is correct
32 Correct 7 ms 1116 KB Output is correct
33 Correct 6 ms 1112 KB Output is correct
34 Correct 10 ms 1116 KB Output is correct

Subtask #5
48.0 / 48.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1116 KB Output is correct
2 Correct 2 ms 1116 KB Output is correct
3 Correct 2 ms 1116 KB Output is correct
4 Correct 2 ms 1116 KB Output is correct
5 Correct 2 ms 1116 KB Output is correct
6 Correct 2 ms 1116 KB Output is correct
7 Correct 2 ms 1116 KB Output is correct
8 Correct 2 ms 1116 KB Output is correct
9 Correct 2 ms 1116 KB Output is correct
10 Correct 2 ms 1264 KB Output is correct
11 Correct 2 ms 1116 KB Output is correct
12 Correct 2 ms 1116 KB Output is correct
13 Correct 2 ms 1116 KB Output is correct
14 Correct 2 ms 1196 KB Output is correct
15 Correct 2 ms 1116 KB Output is correct
16 Correct 2 ms 1116 KB Output is correct
17 Correct 2 ms 1116 KB Output is correct
18 Correct 2 ms 1116 KB Output is correct
19 Correct 2 ms 1260 KB Output is correct
20 Correct 2 ms 1116 KB Output is correct
21 Correct 2 ms 1112 KB Output is correct
22 Correct 3 ms 1116 KB Output is correct
23 Correct 2 ms 1256 KB Output is correct
24 Correct 3 ms 1116 KB Output is correct
25 Correct 3 ms 1264 KB Output is correct
26 Correct 2 ms 1116 KB Output is correct
27 Correct 3 ms 1116 KB Output is correct
28 Correct 5 ms 1112 KB Output is correct
29 Correct 6 ms 1116 KB Output is correct
30 Correct 6 ms 1260 KB Output is correct
31 Correct 5 ms 1116 KB Output is correct
32 Correct 7 ms 1116 KB Output is correct
33 Correct 6 ms 1112 KB Output is correct
34 Correct 10 ms 1116 KB Output is correct
35 Correct 24 ms 1116 KB Output is correct
36 Correct 35 ms 1256 KB Output is correct
37 Correct 24 ms 1116 KB Output is correct
38 Correct 27 ms 1116 KB Output is correct
39 Correct 25 ms 1112 KB Output is correct
40 Correct 41 ms 1116 KB Output is correct