#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(v) v.begin(),v.end()
typedef long long ll;

#include <bits/stdc++.h>
using namespace std;

const int MOD=1e9+7;

ll extGCD(ll a,ll b,ll &x,ll &y){
  if(b==0){
    x=1;
    y=0;
    return a;
  }
  ll d=extGCD(b,a%b,y,x);
  y-=a/b*x;
  return d;
}

int main(){
  int t;
  cin>>t;
  
  while(t--){
    ll n,k,h,y;
    cin>>n>>k>>h>>y;
    
    if(n>h) swap(n,h);
    if(k>h) swap(k,h);
    if(n>k) swap(n,k);
    
    int g=gcd(n,k);
    
    int ans=0;
    for(int i=0;i<=y/h;i++){
      if((y-h*i)%g!=0) continue;
      ll r=(y-h*i)/g;
      ll a=n/g;
      ll b=k/g;    
      
      ll p,q;
      if(extGCD(a,b,p,q)<0) p=-p,q=-q;
      p*=r,q*=r;
      if(q/a<-p/b) continue;
      if(p<=0){
        ans=(ans+q/a+p/b)%MOD;
        if(p%b==0) ans++;
      }
      else if(q<=0){
        ans=(ans+q/a+p/b)%MOD;
        if(q%a==0) ans++;
      }
      else{
        ans=(ans+q/a+p/b+1)%MOD;
      }
    }
    cout<<ans<<endl;
  }
  
  return 0;
}