#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 998244353; //constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; template void chmin(T& a, T b) { a = min(a, b); } template void chmax(T& a, T b) { a = max(a, b); } template void cinarray(vector& v) { rep(i, v.size())cin >> v[i]; } template void coutarray(vector& v) { rep(i, v.size()) { if (i > 0)cout << " "; cout << v[i]; } cout << "\n"; } ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; //if (x == 0)return 0; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { int n; modint() :n(0) { ; } modint(ll m) { if (m < 0 || mod <= m) { m %= mod; if (m < 0)m += mod; } n = m; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1 << 20; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } ll gcd(ll a, ll b) { a = abs(a); b = abs(b); if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } typedef long double ld; typedef pair LDP; const ld eps = 1e-8; const ld pi = acosl(-1.0); template void addv(vector& v, int loc, T val) { if (loc >= v.size())v.resize(loc + 1, 0); v[loc] += val; } /*const int mn = 100005; bool isp[mn]; vector ps; void init() { fill(isp + 2, isp + mn, true); for (int i = 2; i < mn; i++) { if (!isp[i])continue; ps.push_back(i); for (int j = 2 * i; j < mn; j += i) { isp[j] = false; } } }*/ //[,val) template auto prev_itr(set& st, T val) { auto res = st.lower_bound(val); if (res == st.begin())return st.end(); res--; return res; } //[val,) template auto next_itr(set& st, T val) { auto res = st.lower_bound(val); return res; } using mP = pair; int dx[4] = { 1,0,-1,0 }; int dy[4] = { 0,1,0,-1 }; //----------------------------------------- int get_premitive_root() { int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { set fac; int v = mod - 1; for (ll i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < mod; g++) { bool ok = true; for (auto i : fac) if (mod_pow(g, (mod - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } const int proot = get_premitive_root(); typedef vector poly; void dft(poly& f, bool inverse = false) { int n = f.size(); if (n == 1)return; static poly w{ 1 }, iw{ 1 }; for (int m = w.size(); m < n / 2; m *= 2) { modint dw = mod_pow(proot, (mod - 1) / (4 * m)), dwinv = (modint)1 / dw; w.resize(m * 2); iw.resize(m * 2); for (int i = 0; i < m; i++)w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv; } if (!inverse) { for (int m = n; m >>= 1;) { for (int s = 0, k = 0; s < n; s += 2 * m, k++) { for (int i = s; i < s + m; i++) { modint x = f[i], y = f[i + m] * w[k]; f[i] = x + y, f[i + m] = x - y; } } } } else { for (int m = 1; m < n; m *= 2) { for (int s = 0, k = 0; s < n; s += 2 * m, k++) { for (int i = s; i < s + m; i++) { modint x = f[i], y = f[i + m]; f[i] = x + y, f[i + m] = (x - y) * iw[k]; } } } modint n_inv = (modint)1 / (modint)n; for (modint& v : f)v *= n_inv; } } poly multiply(poly g, poly h) { int n = 1; int pi = 0, qi = 0; rep(i, g.size())if (g[i])pi = i; rep(i, h.size())if (h[i])qi = i; int sz = pi + qi + 2; while (n < sz)n *= 2; g.resize(n); h.resize(n); dft(g); dft(h); rep(i, n) { g[i] *= h[i]; } dft(g, true); return g; } poly dp[2][18]; void solve() { int n, a, b; cin >> n >> a >> b; modint p = (modint)a / (modint)b; rep(i, n) { rep(j, 2)dp[j][i].resize((1 << i)+1); } dp[0][0][1] = 1; dp[1][0][0] = 1; rep(i, n - 1) { rep(x, 2)rep(y, 2) { poly r = multiply(dp[x][i], dp[y][i]); if (x == y) { rep(j, dp[x][i+1].size()) { if (j < r.size()) { dp[x][i + 1][j] += r[j]; } } } else { rep(j, dp[0][i + 1].size()) { if (j < r.size()) { dp[0][i + 1][j] += r[j] * p; dp[1][i + 1][j] += r[j] * ((modint)1 - p); } } } } } //cout << dp[1][0][0] << "\n"; //cout << dp[1][1][0] << "\n"; poly ndp = { 1 }; rep(i, n) { poly cur(dp[0][i].size()); rep(j, dp[1][i].size()) { cur[j] += dp[0][i][j] * ((modint)1 - p); cur[j] += dp[1][i][j] * p; } ndp = multiply(ndp, cur); } //coutarray(ndp); rep(i, (1 << n)) { modint ans = 0; if (i < ndp.size())ans = ndp[i]; ans /= comb((1 << n) - 1, i); cout << ans << "\n"; } } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(10); init_f(); //init(); //while(true) //useexpr(); //int t; cin >> t; rep(i, t) solve(); return 0; }