#include<bits/stdc++.h>
using namespace std;
const int mod=1e9+7;
const int mx=1e6+5;
typedef long long ll;
ll fact[mx], f[mx];
ll exp(ll a, ll b, ll m) {
ll r=1;
while(b) {
if(b%2) r=(r*a)%m;
a=(a*a)%m;
b/=2;
}
return r;
}
ll inv(ll a, ll m) {
return exp(a,m-2,m);
}
int binom(int n, int m, int mod) {
ll a=fact[n], b=fact[m], c=fact[n-m];
ll ret=a*inv(b,mod);
ret%=mod;
ret*=inv(c,mod);
ret%=mod;
return ret;
}
ll catalan(int n, int mod) {
ll a=fact[2*n], b=fact[n+1], c=fact[n];
ll ret=a*inv(b,mod);
ret%=mod;
ret*=inv(c,mod);
ret%=mod;
return ret;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
fact[0]=1;
for (int i=1; i<mx; i++)
fact[i]=(fact[i-1]*i)%mod;
ll n,k; cin>>n>>k;
f[0]=1;
for (int i=1; i<=n; i++) {
if(i%2==0) f[i]=f[i-1]*(k+1)%mod;
else {
f[i]=(f[i-1]*(k+1))%mod;
ll add=(exp(k,i/2,mod)*catalan(i/2,mod))%mod;
f[i]=(f[i]+(mod-add))%mod;
}
}
cout << f[n] << endl;
return 0;
}
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
280 ms |
17336 KB |
Output is correct |
| 2 |
Correct |
60 ms |
17336 KB |
Output is correct |
| 3 |
Correct |
673 ms |
17336 KB |
Output is correct |
| 4 |
Correct |
746 ms |
17336 KB |
Output is correct |
| 5 |
Correct |
763 ms |
17336 KB |
Output is correct |
| 6 |
Correct |
423 ms |
17336 KB |
Output is correct |
| 7 |
Correct |
476 ms |
17336 KB |
Output is correct |
| 8 |
Correct |
324 ms |
17336 KB |
Output is correct |
| 9 |
Correct |
138 ms |
17336 KB |
Output is correct |
| 10 |
Correct |
40 ms |
17336 KB |
Output is correct |
| 11 |
Correct |
35 ms |
17336 KB |
Output is correct |
| 12 |
Correct |
687 ms |
17336 KB |
Output is correct |
| 13 |
Correct |
648 ms |
17336 KB |
Output is correct |
| 14 |
Correct |
286 ms |
17336 KB |
Output is correct |
| 15 |
Correct |
307 ms |
17336 KB |
Output is correct |
| 16 |
Correct |
278 ms |
17336 KB |
Output is correct |
| 17 |
Correct |
832 ms |
17336 KB |
Output is correct |
| 18 |
Correct |
858 ms |
17336 KB |
Output is correct |
| 19 |
Correct |
903 ms |
17336 KB |
Output is correct |
| 20 |
Correct |
910 ms |
17336 KB |
Output is correct |
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
254 ms |
17336 KB |
Output is correct |
| 2 |
Correct |
84 ms |
17336 KB |
Output is correct |
| 3 |
Correct |
170 ms |
17336 KB |
Output is correct |
| 4 |
Correct |
824 ms |
17336 KB |
Output is correct |
| 5 |
Correct |
515 ms |
17336 KB |
Output is correct |
| 6 |
Correct |
636 ms |
17336 KB |
Output is correct |
| 7 |
Correct |
441 ms |
17336 KB |
Output is correct |
| 8 |
Correct |
255 ms |
17336 KB |
Output is correct |
| 9 |
Correct |
434 ms |
17336 KB |
Output is correct |
| 10 |
Correct |
61 ms |
17336 KB |
Output is correct |
| 11 |
Correct |
715 ms |
17336 KB |
Output is correct |
| 12 |
Correct |
752 ms |
17336 KB |
Output is correct |
| 13 |
Correct |
702 ms |
17336 KB |
Output is correct |
| 14 |
Correct |
340 ms |
17336 KB |
Output is correct |
| 15 |
Correct |
419 ms |
17336 KB |
Output is correct |
| 16 |
Correct |
418 ms |
17336 KB |
Output is correct |
| 17 |
Correct |
77 ms |
17336 KB |
Output is correct |
| 18 |
Correct |
907 ms |
17336 KB |
Output is correct |
| 19 |
Correct |
912 ms |
17336 KB |
Output is correct |
| 20 |
Correct |
907 ms |
17336 KB |
Output is correct |
