#include #include using namespace std; const long long MOD = 998244353; long long modpow(long long a, long long b){ long long ans = 1; while (b > 0){ if (b % 2 == 1){ ans *= a; ans %= MOD; } a *= a; a %= MOD; b /= 2; } return ans; } long long modinv(long long a){ return modpow(a, MOD - 2); } vector mf = {1}; vector mfi = {1}; long long modfact(int n){ if (mf.size() > n){ return mf[n]; } else { for (int i = mf.size(); i <= n; i++){ long long next = mf.back() * i % MOD; mf.push_back(next); mfi.push_back(modinv(next)); } return mf[n]; } } long long modfactinv(int n){ if (mfi.size() > n){ return mfi[n]; } else { modfact(n); return mfi[n]; } } long long modbinom(int n, int k){ if (n < 0 || k < 0 || k > n){ return 0; } else { return modfact(n) * modfactinv(k) % MOD * modfactinv(n - k) % MOD; } } long long modperm(int n, int k){ if (n < 0 || k < 0 || k > n){ return 0; } else { return modfact(n) * modfactinv(n - k) % MOD; } } int main(){ int N, K, X; cin >> N >> K >> X; K--; X--; long long ans = 0; vector f1(K), f2(K), f3(K); for (int i = 0; i < K; i++){ f1[i] = modfactinv(i) * modperm(X, i) % MOD * modbinom(X - i, 2) % MOD; f2[i] = modfactinv(i) * modperm(X, i) % MOD; f3[i] = modfactinv(i) * modperm(X, i) % MOD * (X - i + 1) % MOD; } vector g1(K), g2(K), g3(K); for (int i = 0; i < K; i++){ g1[i] = modfactinv(i) * modperm(N - X - 1, i) % MOD; g2[i] = modfactinv(i) * modperm(N - X - 1, i) % MOD * modbinom(N - X - 1 - i, 2) % MOD; g3[i] = modfactinv(i) * modperm(N - X - 1, i) % MOD * (N - X - 1 -i) % MOD; } vector h1 = atcoder::convolution(f1, g1); vector h2 = atcoder::convolution(f2, g2); vector h3 = atcoder::convolution(f3, g3); for (int i = 0; i < K; i++){ ans += modfact(i) * modfact(N - 2 - i) % MOD * modfact(N - 1 - i) % MOD * (h1[i] + h2[i] + h3[i]) % MOD; } for (int i = 0; i <= min(K, X - 1); i++){ ans += modbinom(K, i) * modperm(X, i) % MOD * modperm(N - X - 1, K - i) % MOD * (X - i) % MOD * modfact(N - 1 - K) % MOD * modfact(N - 1 - K) % MOD; } for (int i = K + 1; i < N - 1; i++){ ans += modperm(N - 1, i - 1) * modbinom(N - i, 2) % MOD * modfact(N - 1 - i) % MOD * modfact(N - 1 - i) % MOD; } ans %= MOD; cout << ans << endl; }