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Submission #509584

# Submission time Handle Problem Language Result Execution time Memory
509584 2022-01-14T07:06:26 Z Rainbowbunny NoM (RMI21_nom) C++17
100 / 100
 83 ms 384 KB 
#include <bits/stdc++.h>
using namespace std;

const int MAXN = 4005;
const int mod = 1e9 + 7;

int Add(int x, int y)
{
    return x + y >= mod ? x + y - mod : x + y;
}

int Sub(int x, int y)
{
    return x - y < 0 ? x - y + mod : x - y;
}

int Mul(int x, int y)
{
    return 1ll * x * y % mod;
}

int BinPow(int n, int k)
{
    int ans = 1, cur = n;
    while(k)
    {
        if(k & 1)
        {
            ans = Mul(ans, cur);
        }
        cur = Mul(cur, cur);
        k >>= 1;
    }
    return ans;
}

int n, m;
int cnt[MAXN], fact[MAXN], ifact[MAXN], dp[2][MAXN];

int C(int n, int k)
{
    return Mul(fact[n], Mul(ifact[k], ifact[n - k]));
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    fact[0] = 1;
    for(int i = 1; i < MAXN; i++)
    {
        fact[i] = Mul(fact[i - 1], i);
    }
    ifact[MAXN - 1] = BinPow(fact[MAXN - 1], mod - 2);
    for(int i = MAXN - 2; i >= 0; i--)
    {
        ifact[i] = Mul(ifact[i + 1], i + 1);
    }
    cin >> n >> m;
    for(int i = 0; i < 2 * n; i++)
    {
        cnt[i % m]++;
    }
    int cur = 0;
    dp[0][0] = 1;
    for(int i = 0; i < m; i++)
    {
        for(int j = 0; j <= cur; j++)
        {
            if(dp[0][j])
            {
                for(int newpair = 0; 2 * newpair <= cnt[i]; newpair++)
                {
                    dp[1][j + newpair] = Add(dp[1][j + newpair], Mul(dp[0][j], Mul(fact[cnt[i]], Mul(ifact[cnt[i] - 2 * newpair], C(n - j, newpair)))));
                }
            }
        }
        cur += cnt[i];
        for(int j = 0; j <= cur; j++)
        {
            dp[0][j] = dp[1][j];
            dp[1][j] = 0;
        }
    }
    for(int i = n; i >= 0; i--)
    {
        dp[0][i] = Mul(dp[0][i], fact[2 * n - 2 * i]);
        for(int j = i + 1; j <= n; j++)
        {
            dp[0][i] = Sub(dp[0][i], Mul(C(j, i), dp[0][j]));
        }
    }
    cout << dp[0][0] << '\n';
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 0 ms 332 KB Output is correct
7 Correct 0 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 0 ms 332 KB Output is correct
7 Correct 0 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 332 KB Output is correct
13 Correct 0 ms 332 KB Output is correct
14 Correct 0 ms 332 KB Output is correct
15 Correct 1 ms 332 KB Output is correct
16 Correct 1 ms 332 KB Output is correct
17 Correct 1 ms 332 KB Output is correct
18 Correct 1 ms 332 KB Output is correct
19 Correct 1 ms 332 KB Output is correct

Subtask #3
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 0 ms 332 KB Output is correct
7 Correct 0 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 332 KB Output is correct
13 Correct 0 ms 332 KB Output is correct
14 Correct 0 ms 332 KB Output is correct
15 Correct 1 ms 332 KB Output is correct
16 Correct 1 ms 332 KB Output is correct
17 Correct 1 ms 332 KB Output is correct
18 Correct 1 ms 332 KB Output is correct
19 Correct 1 ms 332 KB Output is correct
20 Correct 1 ms 332 KB Output is correct
21 Correct 1 ms 332 KB Output is correct
22 Correct 2 ms 332 KB Output is correct
23 Correct 1 ms 332 KB Output is correct
24 Correct 1 ms 332 KB Output is correct
25 Correct 1 ms 332 KB Output is correct
26 Correct 1 ms 332 KB Output is correct
27 Correct 3 ms 332 KB Output is correct

Subtask #4
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 0 ms 332 KB Output is correct
7 Correct 0 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 332 KB Output is correct
13 Correct 0 ms 332 KB Output is correct
14 Correct 0 ms 332 KB Output is correct
15 Correct 1 ms 332 KB Output is correct
16 Correct 1 ms 332 KB Output is correct
17 Correct 1 ms 332 KB Output is correct
18 Correct 1 ms 332 KB Output is correct
19 Correct 1 ms 332 KB Output is correct
20 Correct 1 ms 332 KB Output is correct
21 Correct 1 ms 332 KB Output is correct
22 Correct 2 ms 332 KB Output is correct
23 Correct 1 ms 332 KB Output is correct
24 Correct 1 ms 332 KB Output is correct
25 Correct 1 ms 332 KB Output is correct
26 Correct 1 ms 332 KB Output is correct
27 Correct 3 ms 332 KB Output is correct
28 Correct 4 ms 332 KB Output is correct
29 Correct 6 ms 332 KB Output is correct
30 Correct 6 ms 332 KB Output is correct
31 Correct 4 ms 332 KB Output is correct
32 Correct 7 ms 332 KB Output is correct
33 Correct 8 ms 364 KB Output is correct
34 Correct 15 ms 332 KB Output is correct

Subtask #5
48.0 / 48.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 0 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 0 ms 332 KB Output is correct
5 Correct 0 ms 332 KB Output is correct
6 Correct 0 ms 332 KB Output is correct
7 Correct 0 ms 332 KB Output is correct
8 Correct 0 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 0 ms 332 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 332 KB Output is correct
13 Correct 0 ms 332 KB Output is correct
14 Correct 0 ms 332 KB Output is correct
15 Correct 1 ms 332 KB Output is correct
16 Correct 1 ms 332 KB Output is correct
17 Correct 1 ms 332 KB Output is correct
18 Correct 1 ms 332 KB Output is correct
19 Correct 1 ms 332 KB Output is correct
20 Correct 1 ms 332 KB Output is correct
21 Correct 1 ms 332 KB Output is correct
22 Correct 2 ms 332 KB Output is correct
23 Correct 1 ms 332 KB Output is correct
24 Correct 1 ms 332 KB Output is correct
25 Correct 1 ms 332 KB Output is correct
26 Correct 1 ms 332 KB Output is correct
27 Correct 3 ms 332 KB Output is correct
28 Correct 4 ms 332 KB Output is correct
29 Correct 6 ms 332 KB Output is correct
30 Correct 6 ms 332 KB Output is correct
31 Correct 4 ms 332 KB Output is correct
32 Correct 7 ms 332 KB Output is correct
33 Correct 8 ms 364 KB Output is correct
34 Correct 15 ms 332 KB Output is correct
35 Correct 25 ms 380 KB Output is correct
36 Correct 50 ms 384 KB Output is correct
37 Correct 26 ms 364 KB Output is correct
38 Correct 37 ms 372 KB Output is correct
39 Correct 64 ms 364 KB Output is correct
40 Correct 83 ms 368 KB Output is correct