#include<bits/stdc++.h>
#define L(i, j, k) for(int i = (j); i <= (k); ++i)
#define R(i, j, k) for(int i = (j); i >= (k); --i)
#define ll long long
#define vi vector <int> 
#define sz(a) ((int) (a).size())
using namespace std;
const int N = 1 << 12;
int mod;
int qpow(int x, int y = mod - 2) {
	int res = 1;
	for(; y; x = (ll) x * x % mod, y >>= 1) if(y & 1) res = (ll) res * x % mod;
	return res;
}
int fac[N], ifac[N], inv[N];
void init(int x) {
	fac[0] = ifac[0] = inv[1] = 1;
	L(i, 2, x) inv[i] = (ll) (mod - mod / i) * inv[mod % i] % mod;
	L(i, 1, x) fac[i] = (ll) fac[i - 1] * i % mod, ifac[i] = (ll) ifac[i - 1] * inv[i] % mod;
} 
int C(int x, int y) {
	return x < y || y < 0 ? 0 : (ll) fac[x] * ifac[y] % mod * ifac[x - y] % mod;
}
int n, k, dp[N][N], pe[N][N], W[N][N], F[N], Z[N][N];
int main () {
	ios :: sync_with_stdio(false);
	cin.tie(0); cout.tie(0);
	cin >> n >> k >> mod;
	init (n);
	L(i, 1, n) {
		L(j, 1, n / i) F[j] = W[i][j] = qpow (ifac[j], (ll) i * k % (mod - 1)); 
		L(j, 1, n / i) L(k, 1, j - 1) (W[i][j] += mod - (ll) W[i][k] * k % mod * inv[j] % mod * F[j - k] % mod) %= mod;
	}
	L(i, 1, n) Z[i][0] = 1;
	L(i, 1, n) {
		L(j, 1, n / i) {
			L(k, 1, i - 1) 
				(Z[j][i - 1] += (ll) Z[j][i - 1 - k] * pe[j][k] % mod * k % mod * inv[i - 1] % mod) %= mod;
			dp[i][j] = (ll) Z[j][i - 1] * qpow (inv[i], (ll) j * k % (mod - 1)) % mod; 
		}
		L(j, 1, n / i) 
			L(k, 1, n / (i * j)) 
				(pe[j][i * k] += (ll) W[j][k] * dp[i][j * k] % mod) %= mod;
	}
	cout << (ll) dp[n][1] * qpow (n, k) % mod << '\n';
	return 0;
}