o=->a,n{n<1?1:a**n[0]*o[a,n/2]**2%M}
eval'N,A,B='+`dd`.split*?,
a=o[A*=t=o[A+B,-2+M=10**9+7],N]
b=o[B*=t,N]
[g=1,*(1...N).map{|i|g=g*i%M}].map{|f|$.=($.+o[g*f,M-2]*(a+b)*100*g*t=t*N%M)%M
N+=1
a=a*B%M
b=b*A%M}
p$.