mod = 998244353 omega = pow(3,119,mod) rev_omega = pow(omega,mod-2,mod) N = 2**18 g1 = [1]*(N+1) # 元テーブル g2 = [1]*(N+1) #逆元テーブル inv = [1]*(N+1) #逆元テーブル計算用テーブル for i in range( 2, N + 1 ): g1[i]=( ( g1[i-1] * i ) % mod ) inv[i]=( ( -inv[mod % i] * (mod//i) ) % mod ) g2[i]=( (g2[i-1] * inv[i]) % mod ) inv[0]=0 def cmb(n,r,mod): if r < 0 or n < r: return 0 return (g1[n] * g2[r] % mod) * g2[n-r] % mod def _ntt(f,L,reverse=False): F=[f[i] for i in range(L)] n = L.bit_length() - 1 base = omega if reverse: base = rev_omega if not n: return F size = 2**n wj = pow(base,2**22,mod) res = [0]*2**n for i in range(n,0,-1): use_omega = pow(base,2**(22+i-n),mod) res = [0]*2**n size //= 2 w = 1 for j in range(0,L//2,size): for a in range(size): res[a+j] = (F[a+2*j] + w * F[a+size+2*j]) % mod t = (w * wj) % mod res[L//2+a+j] = (F[a+2*j] + t * F[a+size+2*j]) % mod w = (w * use_omega) % mod F = res return res def ntt(f,L=0): l = len(f) if not L: L = 1<<((l-1).bit_length()) while len(f) c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353. It returns an empty list if at least one of a and b are empty. Constraints ----------- > len(a) + len(b) <= 8388609 Complexity ---------- > O(n log n), where n = len(a) + len(b). """ n = len(a) m = len(b) if n == 0 or m == 0: return [] if min(n, m) <= 0: return _convolution_naive(a, b) if a is b: return _convolution_square(a) return _convolution_fft(a, b) import sys,random,bisect from collections import deque,defaultdict from heapq import heapify,heappop,heappush from itertools import permutations from math import log,gcd input = lambda :sys.stdin.readline().rstrip() mi = lambda :map(int,input().split()) li = lambda :list(mi()) N,A,B = mi() a = 2*A*pow(B,mod-2,mod) % mod b = (B-2*A) * pow(B,mod-2,mod) % mod f = [0,1] for i in range(N): """ g = convolution(f,f) g = [b*v % mod for v in g] f += [0] * (len(f)-1) for j in range(1,len(f)): f[j] += f[j-1] f[j] %= mod for j in range(len(f)): g[j] += f[j]*2*a % mod g[j] %= mod """ F = [f[j]*cmb(2**i,j,mod) for j in range(2**i+1)] G = convolution(F,F) F += [0] * 2**i H = [cmb(2**i,j,mod) for j in range(2**i+1)] H = convolution(F,H) f = [(H[j]*a%mod+G[j]*b%mod)%mod for j in range(2**(i+1)+1)] f = [f[j]*((g1[j]*g1[2**(i+1)-j] % mod)*g2[2**(i+1)] % mod)%mod for j in range(2**(i+1)+1)] for i in range(1,2**N+1): print((f[i]-f[i-1])%mod)