#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace atcoder; typedef long long ll; typedef vector vl; typedef vector> vvl; typedef pair P; #define rep(i, n) for(ll i = 0; i < n; i++) #define exrep(i, a, b) for(ll i = a; i <= b; i++) #define out(x) cout << x << endl #define exout(x) printf("%.10f\n", x) #define chmax(x, y) x = max(x, y) #define chmin(x, y) x = min(x, y) #define all(a) a.begin(), a.end() #define rall(a) a.rbegin(), a.rend() #define pb push_back #define re0 return 0 const ll mod = 998244353; const ll INF = 1e16; const ll MAX = 300000; ll fact[MAX]; // fact[i] : iの階乗のmod ll inv[MAX]; // inv[i] : iの逆数のmod ll invfact[MAX]; // invfact[i] : iの階乗の逆数のmod void init() { fact[0] = 1; inv[0] = inv[1] = 1; invfact[0] = 1; for(ll i = 1; i < MAX; i++) { fact[i] = i * fact[i-1] % mod; if(i >= 2) { inv[i] = mod - inv[mod % i] * (mod / i) % mod; } invfact[i] = invfact[i-1] * inv[i] % mod; } } // nCrをO(n)で求める。 ll Comb(ll n, ll r) { if(r < 0 || n < 0 || n < r) { return 0; } ll res = fact[n]; res = (res * invfact[r]) % mod; res = (res * invfact[n - r]) % mod; return res; } // a^n (mod.MOD)を求める。計算量はO(logn) ll modpow(ll a, ll n, ll MOD = mod) { if(n == 0) { return 1; } if(n % 2 == 1) { return a * modpow(a, n-1, MOD) % MOD; } return modpow(a, n/2, MOD) * modpow(a, n/2, MOD) % MOD; } int main() { ll n, A, B; cin >> n >> A >> B; init(); ll p = A * modpow(B, mod - 2) % mod; vl two(n+1); // two[i] : 2^i two[0] = 1; exrep(i, 1, n) { two[i] = 2 * two[i-1]; } vvl vec1(n, vl(two[n] + 1)); // vec1[i][m] : 1 / Comb(2^(i+1), m) vvl vec2(n, vl(two[n] + 1)); // vec2[i][m] : 1 / Comb(2^(i+1) - 1, m) rep(i, n) { exrep(m, 0, two[i+1]) { vec1[i][m] = modpow(Comb(two[i+1], m), mod - 2); vec2[i][m] = modpow(Comb(two[i+1] - 1, m), mod - 2); } } vvl g(n+1, vl(two[n] + 1)); // g[i][j] : サイズiのトーナメントに1が含まれず、0がj個のとき0が勝つ確率 g[0][1] = 1; rep(i, n) { vl c(two[i+1] + 1); vl d(two[i+1] + 1); exrep(j, 0, two[i+1]) { c[j] = Comb(two[i], j) * g[i][j] % mod; d[j] = Comb(two[i], j); } vl v1 = convolution(c, c); vl v2 = convolution(c, d); exrep(m, 0, two[i+1]) { g[i+1][m] = ((1 + 2*mod - 2*p) * v1[m] + 2 * p * v2[m]) % mod * vec1[i][m] % mod; } } vvl f(n+1, vl(two[n])); // f[i][j] : サイズiのトーナメントに1が含まれて、0がj個のとき1が勝つ確率 f[0][0] = 1; rep(i, n) { vl a(two[i+1]); vl b(two[i+1]); rep(j, two[i+1]) { a[j] = Comb(two[i] - 1, j) * f[i][j] % mod; b[j] = Comb(two[i], j) * ((1 + 2*mod - 2*p) * g[i][j] % mod + p) % mod; } vl v = convolution(a, b); rep(m, two[i+1]) { f[i+1][m] = v[m] * vec2[i][m] % mod; } } rep(x, two[n]) { cout << f[n][x] << "\n"; } re0; }