#include using namespace std; #define rep(i, n) for (int i=0; i struct NTT{ inline void add(int &a, int b) { a += b; if(a >= md) a -= md; } inline void sub(int &a, int b) { a -= b; if(a < 0) a += md; } inline int mul(int a, int b) { return (int)((ll)a*b%md); } inline int power(int a, long long b) { int res = 1; while (b > 0) { if (b & 1) res = mul(res, a); a = mul(a, a); b >>= 1; } return res; } inline int inv(int a) { a %= md; if (a < 0) a += md; int b = md, u = 0, v = 1; while (a) { int t = b / a; b -= t * a; swap(a, b); u -= t * v; swap(u, v); } assert(b == 1); if (u < 0) u += md; return u; } int max_base, root; vector dw, idw; NTT() { int tmp = md - 1; max_base = 0; while (tmp % 2 == 0) { tmp /= 2; max_base++; } root = 2; while (power(root, (md-1)>>1) == 1) root++; dw.resize(max_base); idw.resize(max_base); rep(i, max_base){ sub(dw[i], power(root, (md-1) >> (i+2))); idw[i] = inv(dw[i]); } } void fft(vector &a, bool inv) { const int n = a.size(); assert((n & (n - 1)) == 0); assert(__builtin_ctz(n) <= max_base); if(!inv){ for(int m=n;m>>=1;){ int w = 1; for(int s=0,k=0; s=y?x-y:x+md-y); a[i] = (x+y>=md?x+y-md:x+y); } w = mul(w, dw[__builtin_ctz(++k)]); } } } else{ for(int m=1;m=y?x-y:x+md-y); a[j] = mul(a[j], w); a[i] = (x+y>=md?x+y-md:x+y); } w = mul(w, idw[__builtin_ctz(++k)]); } } } } vector multiply(vector a, vector b, int eq = 0) { int need = a.size() + b.size() - 1; int nbase = 0; while ((1 << nbase) < need) nbase++; int sz = 1 << nbase; a.resize(sz); b.resize(sz); fft(a, 0); if (eq) b = a; else fft(b, 0); int inv_sz = inv(sz); for (int i = 0; i < sz; i++) { a[i] = mul(mul(a[i], b[i]), inv_sz); } fft(a, 1); a.resize(need); return a; } vector square(vector a) { return multiply(a, a, 1); } }; NTT ntt; vector calc(int k) { vector f = {1}; rep(i, N) f.pb(0); vector g; ll p = 1; for (int i=0; i<=N; i++) {g.pb(finv[i]*(p-1)%MOD); p = 2*p%MOD;} int c = 0; while (k>0) { if (k&1) f = ntt.multiply(f, g); k >>= 1; g = ntt.multiply(g, g); c += 1; while (f.size()>N+1) f.pop_back(); while (g.size()>N+1) g.pop_back(); } return f; } int main() { //ループ変数が被っていないか? //制約を確認しているか? //変数のtypoがないか? cin.tie(0); ios::sync_with_stdio(false); cin >> N >> M >> K; Cinit(); vector f = calc(K); ll ans = 0, p = 1; for (int i=N; i>=0; i--) { ll add = C(N, i)*fact[i]%MOD; add = add*f[i]%MOD; add = add*p%MOD; ans = (ans+add)%MOD; p = (M-K)*p%MOD; } cout << ans*C(M, K)%MOD << endl; }