#include <bits/stdc++.h>
using namespace std;
#define int long long
typedef long long ll;
int n, MOD;
const int MAXN = 31;
int dp[MAXN][MAXN][2];
int fac[MAXN];
int facinv[MAXN];
void free_endings(int i) { // how much stuff is left to allocate
for (int j = 0; j <= n-i; j++) { // only this much stuff can actually exist
for (int a = 0; a < 2; a++) {
dp[i][j][a] = ((ll)dp[i][j][a]*facinv[j])%MOD + (j ? dp[i][j-1][a] : 0);
dp[i][j][a] %= MOD;
}
}
for (int j = 0; j <= n-i; j++) {
for (int a = 0; a < 2; a++)
dp[i][j][a] = ((ll)dp[i][j][a]*fac[j])%MOD;
}
}
int expo(ll a, int b) {
ll cur = 1;
while (b) {
if (b & 1) {
cur = (cur*a)%MOD;
}
a = (a*a)%MOD;
b /= 2;
}
return cur;
}
int inv(int a) {
return expo(a, MOD-2);
}
ll choose(int a, int b) {
ll cur = fac[a]*facinv[b];
cur %= MOD;
return (cur*facinv[a-b])%MOD;
}
signed main() {
cin >> n >> MOD;
fac[0] = facinv[0] = 1;
for (int i = 1; i <= n; i++) {
fac[i] = ((ll)i*fac[i-1])%MOD;
}
facinv[n] = inv(fac[n]);
for (int i = n-1; i > 0; i--) {
facinv[i] = ((ll)(i+1)*facinv[i+1])%MOD;
}
for (int i = 0; i <= n; i++) {
dp[0][i][0] = fac[i];
dp[0][i][1] = fac[i+1];
}
for (int i = 1; i <= n; i++) {
for (int j = 0; j <= n-i; j++) {
for (int a = 0; a <= i-1; a++) {
for (int b = 0; b <= j; b++) {
for (int t1 = 0; t1 < 2; t1++) {
for (int t2 = 0; t2 < 2; t2++) {
if (t2 && a == i-1) continue;
ll cur = (ll)dp[i-a-1-t2][j+a-b][t2]*fac[a+b+t1+t2];;
cur %= MOD;
cur *= choose(j, b); cur %= MOD;
cur *= facinv[a]; cur %= MOD;
// if (i == 3 && j == 0 && t1 == 0)
// cout << a << ' ' << b << ' ' << t2 << ": " << cur << '\n';
dp[i][j][t1] += cur;
dp[i][j][t1] %= MOD;
}
}
}
}
}
free_endings(i);
}
ll oth = 1;
for (int i = 2*n-1; i > 0; i -= 2) {
oth = (oth*i)%MOD;
}
cout << (oth+MOD-dp[n][0][0])%MOD << '\n';
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
468 KB |
Output is correct |
| 2 |
Correct |
1 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
1 ms |
212 KB |
Output is correct |
| 6 |
Correct |
0 ms |
212 KB |
Output is correct |
| 7 |
Correct |
0 ms |
304 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
468 KB |
Output is correct |
| 2 |
Correct |
1 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
1 ms |
212 KB |
Output is correct |
| 6 |
Correct |
0 ms |
212 KB |
Output is correct |
| 7 |
Correct |
0 ms |
304 KB |
Output is correct |
| 8 |
Correct |
1 ms |
304 KB |
Output is correct |
| 9 |
Correct |
1 ms |
212 KB |
Output is correct |
| 10 |
Correct |
0 ms |
212 KB |
Output is correct |
| 11 |
Correct |
1 ms |
300 KB |
Output is correct |
| 12 |
Correct |
1 ms |
212 KB |
Output is correct |
| 13 |
Correct |
0 ms |
212 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
468 KB |
Output is correct |
| 2 |
Correct |
1 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
1 ms |
212 KB |
Output is correct |
| 6 |
Correct |
0 ms |
212 KB |
Output is correct |
| 7 |
Correct |
0 ms |
304 KB |
Output is correct |
| 8 |
Correct |
1 ms |
304 KB |
Output is correct |
| 9 |
Correct |
1 ms |
212 KB |
Output is correct |
| 10 |
Correct |
0 ms |
212 KB |
Output is correct |
| 11 |
Correct |
1 ms |
300 KB |
Output is correct |
| 12 |
Correct |
1 ms |
212 KB |
Output is correct |
| 13 |
Correct |
0 ms |
212 KB |
Output is correct |
| 14 |
Correct |
1 ms |
212 KB |
Output is correct |
| 15 |
Correct |
6 ms |
316 KB |
Output is correct |
| 16 |
Correct |
5 ms |
212 KB |
Output is correct |
| 17 |
Correct |
1 ms |
212 KB |
Output is correct |
| 18 |
Correct |
1 ms |
212 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
468 KB |
Output is correct |
| 2 |
Correct |
1 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
1 ms |
212 KB |
Output is correct |
| 6 |
Correct |
0 ms |
212 KB |
Output is correct |
| 7 |
Correct |
0 ms |
304 KB |
Output is correct |
| 8 |
Correct |
1 ms |
304 KB |
Output is correct |
| 9 |
Correct |
1 ms |
212 KB |
Output is correct |
| 10 |
Correct |
0 ms |
212 KB |
Output is correct |
| 11 |
Correct |
1 ms |
300 KB |
Output is correct |
| 12 |
Correct |
1 ms |
212 KB |
Output is correct |
| 13 |
Correct |
0 ms |
212 KB |
Output is correct |
| 14 |
Correct |
1 ms |
212 KB |
Output is correct |
| 15 |
Correct |
6 ms |
316 KB |
Output is correct |
| 16 |
Correct |
5 ms |
212 KB |
Output is correct |
| 17 |
Correct |
1 ms |
212 KB |
Output is correct |
| 18 |
Correct |
1 ms |
212 KB |
Output is correct |
| 19 |
Runtime error |
1923 ms |
420 KB |
Execution killed with signal 11 |
| 20 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
468 KB |
Output is correct |
| 2 |
Correct |
1 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
1 ms |
212 KB |
Output is correct |
| 6 |
Correct |
0 ms |
212 KB |
Output is correct |
| 7 |
Correct |
0 ms |
304 KB |
Output is correct |
| 8 |
Correct |
1 ms |
304 KB |
Output is correct |
| 9 |
Correct |
1 ms |
212 KB |
Output is correct |
| 10 |
Correct |
0 ms |
212 KB |
Output is correct |
| 11 |
Correct |
1 ms |
300 KB |
Output is correct |
| 12 |
Correct |
1 ms |
212 KB |
Output is correct |
| 13 |
Correct |
0 ms |
212 KB |
Output is correct |
| 14 |
Correct |
1 ms |
212 KB |
Output is correct |
| 15 |
Correct |
6 ms |
316 KB |
Output is correct |
| 16 |
Correct |
5 ms |
212 KB |
Output is correct |
| 17 |
Correct |
1 ms |
212 KB |
Output is correct |
| 18 |
Correct |
1 ms |
212 KB |
Output is correct |
| 19 |
Runtime error |
1923 ms |
420 KB |
Execution killed with signal 11 |
| 20 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
468 KB |
Output is correct |
| 2 |
Correct |
1 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
1 ms |
212 KB |
Output is correct |
| 6 |
Correct |
0 ms |
212 KB |
Output is correct |
| 7 |
Correct |
0 ms |
304 KB |
Output is correct |
| 8 |
Correct |
1 ms |
304 KB |
Output is correct |
| 9 |
Correct |
1 ms |
212 KB |
Output is correct |
| 10 |
Correct |
0 ms |
212 KB |
Output is correct |
| 11 |
Correct |
1 ms |
300 KB |
Output is correct |
| 12 |
Correct |
1 ms |
212 KB |
Output is correct |
| 13 |
Correct |
0 ms |
212 KB |
Output is correct |
| 14 |
Correct |
1 ms |
212 KB |
Output is correct |
| 15 |
Correct |
6 ms |
316 KB |
Output is correct |
| 16 |
Correct |
5 ms |
212 KB |
Output is correct |
| 17 |
Correct |
1 ms |
212 KB |
Output is correct |
| 18 |
Correct |
1 ms |
212 KB |
Output is correct |
| 19 |
Runtime error |
1923 ms |
420 KB |
Execution killed with signal 11 |
| 20 |
Halted |
0 ms |
0 KB |
- |
