#include<bits/stdc++.h>
#include<atcoder/all>
using namespace atcoder;
using namespace std;
using ll = long long;
using mint = modint1000000007;
long long extGCD(long long a, long long b, long long &x, long long &y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    long long d = extGCD(b, a%b, y, x);
    y -= a/b * x;
    return d;
}
int main(){
	int t = 1;
	cin >> t;
	while(t--){
		ll N,K,H,Y;
		cin >> N >> K >> H >> Y;
		vector<ll> A={N,K,H};
		sort(A.begin(),A.end(),greater<>());
		ll x,y;
		mint ans = 0;
		for(ll i = 0;i*A[0]<=Y;i++){
			if(i*A[0]==Y){ans++;continue;}
			ll gcd = extGCD(A[1],A[2],x,y);
			if((Y-i*A[0])%gcd!=0)continue;
			x *= (Y-i*A[0])/gcd;y *= (Y-i*A[0])/gcd;
			//X = x + A2 * t;
			//Y = y - A1 * t;
			ll A1 = A[1]/gcd,A2 = A[2]/gcd;
			ll X = -x/A2,Y = y/A1;
			//while(x+A2*X<0)X++;
			ll l = INT_MIN,r= INT_MAX;
			while(r-l>1){
				ll m = (l+r)/2;
				if(y-A1*m<0)r = m;
				else l = m;
			}
			//cout<<l<<' '<<r<<endl;
			//if(y-A1*Y<0)
			Y = l;
			if(Y-X<0)continue;
			ans += Y-X+1;

		}
		cout<<ans.val()<<endl;

	}
}