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Submission #509640

# Submission time Handle Problem Language Result Execution time Memory
509640 2022-01-14T07:45:44 Z duchung NoM (RMI21_nom) C++17
100 / 100
 164 ms 165256 KB 
#include<bits/stdc++.h>
using namespace std;

#define int long long
const int mod = 1e9 + 7;
const int N = 4005;

int n , m;
int fact[N] , inv[N] , cnt[N] , pre[N];
int C[N][N] , dp[N][N];

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 x * y % mod;
}

int binpow(int n , int k)
{
	int ret = 1;
	while(k)
	{
		if (k & 1) ret = Mul(ret , n);
		n = Mul(n , n);
		k >>= 1;
	}
	return ret;
}

void build()
{
	fact[0] = 1;
	for (int i = 1 ; i < N ; ++i) fact[i] = Mul(fact[i - 1] , i);
	inv[0] = 1;
	for (int i = 1 ; i < N ; ++i) inv[i] = binpow(fact[i] , mod - 2);

	for (int i = 0 ; i < 2 * n ; ++i) cnt[i % m + 1]++;
	// for (int i = 1 ; i < m ; ++i) pre[i] = pre[i - 1] + cnt[i];

	C[0][0] = 1;
	for (int i = 1 ; i < N ; ++i)
	{
		C[i][0] = 1;
		for (int j = 1 ; j < N ; ++j) C[i][j] = Add(C[i - 1][j] , C[i - 1][j - 1]);
	}
}

signed main()
{
	// freopen("input.inp","r",stdin);
	// freopen("output.out","w",stdout);
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);

	cin >> n >> m;
	build();

	dp[0][0] = 1;
	for (int i = 1 ; i <= m ; ++i)
	{
		for (int j = 0 ; j <= n ; ++j)
		{
			for (int k = 0 ; 2 * k <= cnt[i] && k <= j ; ++k)
			{
				int cur = dp[i - 1][j - k];
				cur = Mul(cur , fact[cnt[i]]);
				cur = Mul(cur , inv[cnt[i] - k * 2]);
				cur = Mul(cur , C[j][k]);
				dp[i][j] = Add(dp[i][j] , cur);
			}
		}
	}
	
	int ans = 0;
	for (int j = 0 ; j <= n ; ++j)
	{
		if (j & 1) ans = Sub(ans , Mul(fact[n * 2 - j * 2] , Mul(C[n][j] , dp[m][j])));
		else ans = Add(ans , Mul(fact[n * 2 - j * 2] , Mul(C[n][j] , dp[m][j])));
	}
	cout << ans;
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 59 ms 125832 KB Output is correct
2 Correct 62 ms 125820 KB Output is correct
3 Correct 66 ms 125816 KB Output is correct
4 Correct 71 ms 125856 KB Output is correct
5 Correct 60 ms 126020 KB Output is correct
6 Correct 62 ms 125836 KB Output is correct
7 Correct 59 ms 125836 KB Output is correct
8 Correct 61 ms 125872 KB Output is correct
9 Correct 59 ms 125796 KB Output is correct
10 Correct 60 ms 125816 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 59 ms 125832 KB Output is correct
2 Correct 62 ms 125820 KB Output is correct
3 Correct 66 ms 125816 KB Output is correct
4 Correct 71 ms 125856 KB Output is correct
5 Correct 60 ms 126020 KB Output is correct
6 Correct 62 ms 125836 KB Output is correct
7 Correct 59 ms 125836 KB Output is correct
8 Correct 61 ms 125872 KB Output is correct
9 Correct 59 ms 125796 KB Output is correct
10 Correct 60 ms 125816 KB Output is correct
11 Correct 61 ms 126080 KB Output is correct
12 Correct 60 ms 126020 KB Output is correct
13 Correct 59 ms 125888 KB Output is correct
14 Correct 60 ms 126008 KB Output is correct
15 Correct 59 ms 126160 KB Output is correct
16 Correct 60 ms 125936 KB Output is correct
17 Correct 59 ms 125936 KB Output is correct
18 Correct 72 ms 126112 KB Output is correct
19 Correct 63 ms 125884 KB Output is correct

Subtask #3
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 59 ms 125832 KB Output is correct
2 Correct 62 ms 125820 KB Output is correct
3 Correct 66 ms 125816 KB Output is correct
4 Correct 71 ms 125856 KB Output is correct
5 Correct 60 ms 126020 KB Output is correct
6 Correct 62 ms 125836 KB Output is correct
7 Correct 59 ms 125836 KB Output is correct
8 Correct 61 ms 125872 KB Output is correct
9 Correct 59 ms 125796 KB Output is correct
10 Correct 60 ms 125816 KB Output is correct
11 Correct 61 ms 126080 KB Output is correct
12 Correct 60 ms 126020 KB Output is correct
13 Correct 59 ms 125888 KB Output is correct
14 Correct 60 ms 126008 KB Output is correct
15 Correct 59 ms 126160 KB Output is correct
16 Correct 60 ms 125936 KB Output is correct
17 Correct 59 ms 125936 KB Output is correct
18 Correct 72 ms 126112 KB Output is correct
19 Correct 63 ms 125884 KB Output is correct
20 Correct 62 ms 125980 KB Output is correct
21 Correct 60 ms 126248 KB Output is correct
22 Correct 60 ms 127420 KB Output is correct
23 Correct 62 ms 125936 KB Output is correct
24 Correct 62 ms 126716 KB Output is correct
25 Correct 71 ms 127412 KB Output is correct
26 Correct 68 ms 125892 KB Output is correct
27 Correct 80 ms 127744 KB Output is correct

Subtask #4
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 59 ms 125832 KB Output is correct
2 Correct 62 ms 125820 KB Output is correct
3 Correct 66 ms 125816 KB Output is correct
4 Correct 71 ms 125856 KB Output is correct
5 Correct 60 ms 126020 KB Output is correct
6 Correct 62 ms 125836 KB Output is correct
7 Correct 59 ms 125836 KB Output is correct
8 Correct 61 ms 125872 KB Output is correct
9 Correct 59 ms 125796 KB Output is correct
10 Correct 60 ms 125816 KB Output is correct
11 Correct 61 ms 126080 KB Output is correct
12 Correct 60 ms 126020 KB Output is correct
13 Correct 59 ms 125888 KB Output is correct
14 Correct 60 ms 126008 KB Output is correct
15 Correct 59 ms 126160 KB Output is correct
16 Correct 60 ms 125936 KB Output is correct
17 Correct 59 ms 125936 KB Output is correct
18 Correct 72 ms 126112 KB Output is correct
19 Correct 63 ms 125884 KB Output is correct
20 Correct 62 ms 125980 KB Output is correct
21 Correct 60 ms 126248 KB Output is correct
22 Correct 60 ms 127420 KB Output is correct
23 Correct 62 ms 125936 KB Output is correct
24 Correct 62 ms 126716 KB Output is correct
25 Correct 71 ms 127412 KB Output is correct
26 Correct 68 ms 125892 KB Output is correct
27 Correct 80 ms 127744 KB Output is correct
28 Correct 73 ms 125996 KB Output is correct
29 Correct 81 ms 128784 KB Output is correct
30 Correct 78 ms 131200 KB Output is correct
31 Correct 68 ms 125908 KB Output is correct
32 Correct 67 ms 129096 KB Output is correct
33 Correct 70 ms 131992 KB Output is correct
34 Correct 77 ms 135800 KB Output is correct

Subtask #5
48.0 / 48.0

# Verdict Execution time Memory Grader output
1 Correct 59 ms 125832 KB Output is correct
2 Correct 62 ms 125820 KB Output is correct
3 Correct 66 ms 125816 KB Output is correct
4 Correct 71 ms 125856 KB Output is correct
5 Correct 60 ms 126020 KB Output is correct
6 Correct 62 ms 125836 KB Output is correct
7 Correct 59 ms 125836 KB Output is correct
8 Correct 61 ms 125872 KB Output is correct
9 Correct 59 ms 125796 KB Output is correct
10 Correct 60 ms 125816 KB Output is correct
11 Correct 61 ms 126080 KB Output is correct
12 Correct 60 ms 126020 KB Output is correct
13 Correct 59 ms 125888 KB Output is correct
14 Correct 60 ms 126008 KB Output is correct
15 Correct 59 ms 126160 KB Output is correct
16 Correct 60 ms 125936 KB Output is correct
17 Correct 59 ms 125936 KB Output is correct
18 Correct 72 ms 126112 KB Output is correct
19 Correct 63 ms 125884 KB Output is correct
20 Correct 62 ms 125980 KB Output is correct
21 Correct 60 ms 126248 KB Output is correct
22 Correct 60 ms 127420 KB Output is correct
23 Correct 62 ms 125936 KB Output is correct
24 Correct 62 ms 126716 KB Output is correct
25 Correct 71 ms 127412 KB Output is correct
26 Correct 68 ms 125892 KB Output is correct
27 Correct 80 ms 127744 KB Output is correct
28 Correct 73 ms 125996 KB Output is correct
29 Correct 81 ms 128784 KB Output is correct
30 Correct 78 ms 131200 KB Output is correct
31 Correct 68 ms 125908 KB Output is correct
32 Correct 67 ms 129096 KB Output is correct
33 Correct 70 ms 131992 KB Output is correct
34 Correct 77 ms 135800 KB Output is correct
35 Correct 80 ms 126228 KB Output is correct
36 Correct 159 ms 156172 KB Output is correct
37 Correct 79 ms 126108 KB Output is correct
38 Correct 103 ms 139720 KB Output is correct
39 Correct 124 ms 150428 KB Output is correct
40 Correct 164 ms 165256 KB Output is correct