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Submission #871348

# Submission time Handle Problem Language Result Execution time Memory
871348 2023-11-10T15:44:37 Z TAhmed33 NoM (RMI21_nom) C++
100 / 100
 92 ms 23924 KB 
#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;
int add (int a, int b) {
	a += b; if (a >= MOD) a -= MOD;
	return a;
}
int sub (int a, int b) {
	a -= b; if (a < 0) a += MOD;
	return a;
}
int mul (int a, int b) {
	return (a * 1ll * b) % MOD;
}
int power (int a, int b) {
	if (!b) return 1;
	int u = power(a, b >> 1);
	u = mul(u, u);
	if (b & 1) u = mul(u, a);
	return u;
}
const int MAXN = 5e3 + 25;
int fact[MAXN], inv[MAXN];
void pre () {
	fact[0] = 1;
	for (int i = 1; i < MAXN; i++) {
		fact[i] = mul(i, fact[i - 1]);
	}
	inv[MAXN - 1] = power(fact[MAXN - 1], MOD - 2);
	for (int i = MAXN - 2; i >= 0; i--) {
		inv[i] = mul(i + 1, inv[i + 1]);
	}
}
int nCr (int a, int b) {
	return mul(fact[a], mul(inv[b], inv[a - b]));
}
int nPr (int a, int b) {
	return mul(fact[a], inv[a - b]);
}
int dp[MAXN][MAXN];
int main () {
	pre();
	int n, m;
	cin >> n >> m;
	dp[0][0] = 1;
	int dd[m + 1] = {}; for (int i = 1; i <= 2 * n; i++) dd[i % m]++;
	dd[m] = dd[0];
	for (int i = 0; i <= n; i++) {
		for (int j = 1; j <= m; j++) {
			for (int l = 0; l <= min(i, dd[j] / 2); l++) {
				dp[i][j] = add(dp[i][j], mul(dp[i - l][j - 1], mul(nPr(dd[j], 2 * l), nCr(i, l))));
			}
		}
	}
	int sum = 0;
	for (int i = 1; i <= n; i++) {
		int x = dp[i][m];
		x = mul(x, nCr(n, i));
		x = mul(x, fact[2 * n - 2 * i]);
		if ((i & 1)) sum = sub(sum, x);
		else sum = add(sum, x);
	}	
	cout << add(fact[2 * n], sum) << '\n';
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 484 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 484 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 740 KB Output is correct
12 Correct 1 ms 604 KB Output is correct
13 Correct 1 ms 604 KB Output is correct
14 Correct 1 ms 604 KB Output is correct
15 Correct 1 ms 604 KB Output is correct
16 Correct 1 ms 604 KB Output is correct
17 Correct 1 ms 604 KB Output is correct
18 Correct 1 ms 604 KB Output is correct
19 Correct 1 ms 604 KB Output is correct

Subtask #3
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 484 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 740 KB Output is correct
12 Correct 1 ms 604 KB Output is correct
13 Correct 1 ms 604 KB Output is correct
14 Correct 1 ms 604 KB Output is correct
15 Correct 1 ms 604 KB Output is correct
16 Correct 1 ms 604 KB Output is correct
17 Correct 1 ms 604 KB Output is correct
18 Correct 1 ms 604 KB Output is correct
19 Correct 1 ms 604 KB Output is correct
20 Correct 1 ms 1112 KB Output is correct
21 Correct 1 ms 1116 KB Output is correct
22 Correct 2 ms 1628 KB Output is correct
23 Correct 1 ms 1372 KB Output is correct
24 Correct 2 ms 1628 KB Output is correct
25 Correct 2 ms 1628 KB Output is correct
26 Correct 1 ms 1372 KB Output is correct
27 Correct 3 ms 1884 KB Output is correct

Subtask #4
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 484 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 740 KB Output is correct
12 Correct 1 ms 604 KB Output is correct
13 Correct 1 ms 604 KB Output is correct
14 Correct 1 ms 604 KB Output is correct
15 Correct 1 ms 604 KB Output is correct
16 Correct 1 ms 604 KB Output is correct
17 Correct 1 ms 604 KB Output is correct
18 Correct 1 ms 604 KB Output is correct
19 Correct 1 ms 604 KB Output is correct
20 Correct 1 ms 1112 KB Output is correct
21 Correct 1 ms 1116 KB Output is correct
22 Correct 2 ms 1628 KB Output is correct
23 Correct 1 ms 1372 KB Output is correct
24 Correct 2 ms 1628 KB Output is correct
25 Correct 2 ms 1628 KB Output is correct
26 Correct 1 ms 1372 KB Output is correct
27 Correct 3 ms 1884 KB Output is correct
28 Correct 5 ms 2908 KB Output is correct
29 Correct 8 ms 3932 KB Output is correct
30 Correct 10 ms 4440 KB Output is correct
31 Correct 5 ms 2908 KB Output is correct
32 Correct 9 ms 4032 KB Output is correct
33 Correct 12 ms 4956 KB Output is correct
34 Correct 21 ms 7204 KB Output is correct

Subtask #5
48.0 / 48.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 484 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 740 KB Output is correct
12 Correct 1 ms 604 KB Output is correct
13 Correct 1 ms 604 KB Output is correct
14 Correct 1 ms 604 KB Output is correct
15 Correct 1 ms 604 KB Output is correct
16 Correct 1 ms 604 KB Output is correct
17 Correct 1 ms 604 KB Output is correct
18 Correct 1 ms 604 KB Output is correct
19 Correct 1 ms 604 KB Output is correct
20 Correct 1 ms 1112 KB Output is correct
21 Correct 1 ms 1116 KB Output is correct
22 Correct 2 ms 1628 KB Output is correct
23 Correct 1 ms 1372 KB Output is correct
24 Correct 2 ms 1628 KB Output is correct
25 Correct 2 ms 1628 KB Output is correct
26 Correct 1 ms 1372 KB Output is correct
27 Correct 3 ms 1884 KB Output is correct
28 Correct 5 ms 2908 KB Output is correct
29 Correct 8 ms 3932 KB Output is correct
30 Correct 10 ms 4440 KB Output is correct
31 Correct 5 ms 2908 KB Output is correct
32 Correct 9 ms 4032 KB Output is correct
33 Correct 12 ms 4956 KB Output is correct
34 Correct 21 ms 7204 KB Output is correct
35 Correct 29 ms 7136 KB Output is correct
36 Correct 72 ms 19304 KB Output is correct
37 Correct 28 ms 7000 KB Output is correct
38 Correct 45 ms 12208 KB Output is correct
39 Correct 56 ms 15952 KB Output is correct
40 Correct 92 ms 23924 KB Output is correct