import sys sys.setrecursionlimit(200005) int1 = lambda x: int(x)-1 p2D = lambda x: print(*x, sep="\n") def II(): return int(sys.stdin.buffer.readline()) def LI(): return list(map(int, sys.stdin.buffer.readline().split())) def LI1(): return list(map(int1, sys.stdin.buffer.readline().split())) def LLI(rows_number): return [LI() for _ in range(rows_number)] def LLI1(rows_number): return [LI1() for _ in range(rows_number)] def BI(): return sys.stdin.buffer.readline().rstrip() def SI(): return sys.stdin.buffer.readline().rstrip().decode() dij = [(0, 1), (-1, 0), (0, -1), (1, 0)] # dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)] inf = 10**16 md = 998244353 # md = 10**9+7 import numpy as np from time import time # def dot(aa,bb): # return [[sum(a*b%md for a,b in zip(row,col))%md for col in zip(*bb)] for row in aa] ma, na, s = LI() mb, nb, t = LI() K = II() tt=[] tt.append(time()) s += t s, t = t, s pa = ma*pow(na, md-2, md) pb = mb*pow(nb, md-2, md) # print(pa,pb) dtop = [0]*(t+1) now = (1-pa)%md for i in range(t+1): dtop[i] = now now = now*pa%md pp0=[[0]*(t+1) for _ in range(t+1)] for i in range(1,t): p=1 d=0 for j in range(i,t): pp0[i][j]=dtop[d] p-=dtop[d] d+=1 pp0[i][t]=p%md # p2D(pp0) tt.append(time()) dtop = [0]*(t+1) now = (1-pb)%md for i in range(t+1): dtop[i] = now now = now*pb%md pp1=[[0]*(t+1) for _ in range(t+1)] for i in range(t-1,0,-1): p=1 d=0 for j in range(i,0,-1): pp1[i][j]=dtop[d] p-=dtop[d] d+=1 pp1[i][0]=p%md tt.append(time()) base=np.zeros((t+1,t+1),dtype=object) # base=[[0]*(t+1) for _ in range(t+1)] for i in range(1,t): for j in range(i,t): for k in range(j+1): base[k][i]=(base[k][i]+pp0[i][j]*pp1[j][k])%md for i in range(1,t): base[t][i]=pp0[i][t] base[0][0]=1 base[t][t]=1 # p2D(base) tt.append(time()) # cc=[[0]*(t+1) for _ in range(t+1)] # for i in range(t+1):cc[i][i]=1 cc=np.eye(t+1,dtype=object) while K: if K&1:cc=np.dot(cc,base)%md base=np.dot(base,base)%md K>>=1 tt.append(time()) # print(s,t) # p2D(cc) print(cc[t][s]) print(cc[0][s]) # t0=tt[0] # tt=[t-t0 for t in tt] # print(*tt)