1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
#include <bits/stdc++.h>

using namespace std;

const int N = 1002;
const int K = 12;

const long long LIMIT = 6LL * 1000LL * 1000LL * 1000LL * 1000LL * 1000LL * 1000LL;

int binom[N][N];

long long tmp[K][3];
int dp[N][K][3];

int add(int x, int y, int p) {
    x += y;
    if (x >= p) {
        x -= p;
    }

    return x;
}

void pre(int p) {
    for (int i = 0; i < N; i++) {
        binom[i][0] = 1;
    }

    for (int i = 1; i < N; i++) for (int j = 1; j <= i; j++) {
        binom[i][j] = add(binom[i-1][j], binom[i-1][j-1], p);
    }

    for (int b = 0; b < 3; b++) {
        dp[0][0][b] = 1;
        dp[1][0][b] = b == 0;
        dp[1][1][b] = b != 0;
    }

    for (int n = 2; n < N; n++) {
        for (int n1 = 0; n1 < n; n1++) {
            int n2 = n - 1 - n1;
            int ways = binom[n-1][n1];

            for (int k = 0; k < K; k++) for (int b = 0; b < 3; b++) {
                tmp[k][b] = 0;
            }

            for (int k1 = 0; k1 < K; k1++) for (int bLeft = 0; bLeft < 2; bLeft++) {
                if (!dp[n1][k1][bLeft + 1]) {
                    continue;
                }

                for (int k2 = 0; k2 < K; k2++) for (int bRight = bLeft; bRight < 2; bRight++) {
                    if (!dp[n2][k2][bRight + 1]) {
                        continue;
                    }

                    int k;
                    if (bLeft && bRight) {
                        k = max(k1, k2) + (k1 == k2);
                    } else {
                        k = max(k1 + bLeft, k2 + bRight);
                    }

                    tmp[k][bLeft + bRight] += (long long) dp[n1][k1][bLeft + 1] * dp[n2][k2][bRight + 1];
                    if (tmp[k][bLeft + bRight] >= LIMIT) {
                        tmp[k][bLeft + bRight] %= p;
                    }
                }
            }

            for (int k = 0; k < K; k++) for (int b = 0; b < 3; b++) {
                if (tmp[k][b] >= p) {
                    tmp[k][b] %= p;
                }

                dp[n][k][b] = (dp[n][k][b] + (long long) ways * tmp[k][b]) % p;
            }
        }
    }
}

int solve(int n, int k, int p) {
    if (k >= K) {
        return 0;
    }

    return dp[n][k][0];
}

int main() {
    ios_base::sync_with_stdio(0);

    int n, k, p;
    cin >> n >> k >> p;

    pre(p);
    cout << solve(n, k, p);

    return 0;
}