#include #include using namespace std; using namespace atcoder; istream &operator>>(istream &is, modint &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint &a) { return os << a.val(); } istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); } istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); } typedef long long ll; typedef vector> Graph; typedef pair pii; typedef pair pll; #define FOR(i,l,r) for (int i = l;i < (int)(r); i++) #define rep(i,n) for (int i = 0;i < (int)(n); i++) #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define my_sort(x) sort(x.begin(), x.end()) #define my_max(x) *max_element(all(x)) #define my_min(x) *min_element(all(x)) template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } const int INF = (1<<30) - 1; const ll LINF = (1LL<<62) - 1; const double PI = acos(-1); vector di = {1,0,-1,0}; vector dj = {0,1,0,-1}; #ifdef LOCAL # include # define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else # define debug(...) (static_cast(0)) #endif using mint = modint; int main(){ cin.tie(0); ios_base::sync_with_stdio(false); ll N, M, P; cin >> N >> M >> P; mint::set_mod(P); vector fac(N + 1, 1), finv(N + 1, 1); for(int i = 1; i <= N; i++) { fac[i] = fac[i - 1] * (mint)i; finv[i] = (mint)1 / (mint)fac[i]; } auto nCr = [&](int n, int k){ return fac[n] * finv[k] * finv[n-k]; }; auto nPr = [&](int n, int k){ return fac[n] * finv[n-k]; }; mint ans = 0; vector prv(N + 1); for(int j = 1; j <= M; j++){ vector coef(N + 1); if(j == 1) { for(ll n = 1; n <= N; n++){ coef[n] = (n * (n + 1LL) / 2LL) % P; } } else{ coef[0] = 0; for(ll n = 1; n <= N; n++){ coef[n] = coef[n - 1] + prv[n - 1] * (mint)n; } } ans += coef[N] * nCr(M, j) / nPr(N, j); swap(prv, coef); } cout << ans << endl; }