import math
for _ in[0]*int(input()):
 D,A,B,K=map(int,input().split());g=math.gcd(D,A);D//=g;A//=g;l,h=0,A*B*K+2
 if A*B%D<1 and D*K+2>A:print(-1);continue
 while l+1<h:
  x=n=(l+h)//2;a,b,c,m=B,-(A*B//D),D,A;s=v=d=0
  while(n):a+=c//m*b;c%=m;s+=d//m*b;d%=m;v=max(v,s,s+a*(n-1)+b*(n:=(c*(n-1)+d)//m));s+=(a+b)*(a<0);a,b,c,d,m=b,a,m,m+~d,c
  if v<=B*K:l=x
  else:h=x
 print(g*D*l)