#include #include #include using namespace std; const int MOD = 998244353; long long modPow(long long a, long long p){ if(p == 0) return 1; auto res = modPow(a, p/2); res = (res*res)%MOD; if(p%2) res = (res*a)%MOD; return res; } long long calcInv(long long a){ return modPow(a, MOD-2); } int main(){ const int maxSize = 1025; vector inv(maxSize); vector fact(maxSize); vector factInv(maxSize); for(int i=0;i<2;i++) inv[i] = fact[i] = factInv[i] = 1; for(int i=2;i> N >> K >> X >> Y){ X = min(X, 1023); Y = min(Y, 1023); vector A(K); for(auto& t : A) cin >> t; sort(A.begin(), A.end()); A.erase(unique(A.begin(), A.end()), A.end()); vector valid(N+1, vector(1024, 0)); valid[0][0] = 1; for(auto& v : A){ for(int i=N-1;i>=0;i--){ for(int j=0;j<1024;j++) valid[i+1][j^v] = (valid[i+1][j^v] + valid[i][j]) % MOD; } } vector dp(2, vector(A.size()+1, 0LL)); dp[1][0] = 1; for(int i=0;i 0){ next[1][n1+1] += n0 * dp[1][n1] + (n0-1) * dp[0][n1]; next[1][n1+1] %= MOD; } if(n1 > 0){ next[0][n1-1] += n1 * dp[0][n1] + (n1-1) * dp[1][n1]; next[0][n1-1] %= MOD; } } dp = next; } long long res = 0; for(int i=0;i<=N;i++){ if(i >= dp[0].size()) break; auto pat = (dp[0][i] + dp[1][i]) % MOD; for(int j=X;j<=Y;j++){ res += pat * valid[i][j] % MOD * calcInv(comb(A.size(), i)); res %= MOD; } } cout << res << endl; } }