Find the number of the possible tuples of sequences (A_0,A_1,...,A_N) that satisfy all of the following conditions, modulo M:

* For every i (0\leq i\leq N), A_i is a sequence of length i consisting of integers between 1 and K (inclusive);
* For every i (1\leq i\leq N), A_{i-1} is a subsequence of A_i, that is, there exists 1\leq x_i\leq i such that the removal of the x_i-th element of A_i would result in a sequence equal to A_{i-1};
* For every i (1\leq i\leq N), A_i is lexicographically larger than A_{i-1}.

Constraints

* 1 \leq N,K \leq 300
* 2 \leq M \leq 10^9
* N, K and M are integers.

Input

Input is given from Standard Input in the following format:


N K M


Output

Print the number of the possible tuples of sequences (A_0,A_1,...,A_N), modulo M.

Examples

Input

2 2 100


Output

5


Input

4 3 999999999


Output

358


Input

150 150 998244353


Output

186248260
#include <cstdio>
#include <algorithm>

using namespace std;

typedef long long ll;
const int maxn = 400;
ll C[maxn][maxn] , dp[maxn][maxn] , sum[maxn][maxn];
int n,K,mod;
int main(){
    scanf("%d%d%d",&n,&K,&mod);
    C[0][0] = 1;
    for(int i = 1;i <= n;i++){
        C[i][0] = 1;
        for(int j = 1;j <= i;j++){
            C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % mod;
        }
    }
    for(int j = 0;j <= K;j++) dp[1][j] = 1, sum[1][j] = K - j + 1;
    for(int i = 2;i <= n + 1;i++){
        for(int j = 0;j <= K;j++){
            for(int k = 1;k < i;k++){
                dp[i][j] = (dp[i][j] +  dp[i - k][j]  * sum[k][j + 1] % mod * C[i - 2][k - 1]) % mod;
            }
        }
        for(int j = K;j >= 0;j--) sum[i][j] = (sum[i][j + 1] + dp[i][j]) % mod;
    }
    printf("%lld",dp[n + 1][0]);
}
