using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
using System.Threading;
using System.Runtime.CompilerServices;
using System.Diagnostics;
//using nint=System.Int32;
static class Program{
	const int mod=(int)1e9+7;
	static void Main(){
		Sc sc=new Sc();
		var t=sc.I;
		StringBuilder sb=new StringBuilder();
		for(int i = 0;i < t;i++) {
			var s=sc.La;
			var h=new long[]{s[0],s[1],s[2]};
			Array.Sort(h);
			Extgcd(h[0],h[1],out long x,out long y);
			var g=Gcd(h[0],h[1]);
			Mint ans=0;
			for(int j = 0;j*h[2]<=s[3];j++) {
				var p=s[3]-j*h[2];
				if(p%g!=0){continue;}
				var cc=p/g;
				var xx=x*cc;
				var yy=y*cc;
				var ag=h[0]/g;
				var bg=h[1]/g;
				BigInteger f1=mod;
				BigInteger f2=mod;
				f1=(-xx+bg-1+f1*bg)/bg-mod;
				f2=(yy+f2*ag)/ag-mod;
				ans+=(long)(f2-f1+1)%mod;
			}
			sb.Append(ans+"\n");
		}
		Console.Write(sb);
	}
	static long Gcd(long a,long b){
		long c=Max(a,b)%(b=Min(a,b));
		while(c!=0){
			a=b%c;
			b=c;
			c=a;
		}
		return b;
	}
	static long Extgcd(long a,long b,out long x,out long y) {
		if(b==0){x=1;y=0;return a;}
		long d=Extgcd(b,a%b,out y,out x);
		y-=a/b*x;
		return d;
	}
}
public struct Mint{
	const int mod=(int)1e9+7;
	private long d;
	public Mint(long d){this.d=d;}
	public static implicit operator Mint(long d){return new Mint(d%mod);}
	public static explicit operator long(Mint d){return d.d;}
	public override string ToString(){return d.ToString();}
	public static Mint operator+(Mint a,long b){a.d=(a.d+b)%mod;return a;}
	public static Mint operator+(Mint a,Mint b){a.d=(a.d+b.d)%mod;return a;}
	public static Mint operator-(Mint a,long b){a.d=(mod+a.d-b)%mod;return a;}
	public static Mint operator-(Mint a,Mint b){a.d=(mod+a.d-b.d)%mod;return a;}
	public static Mint operator*(Mint a,long b){a.d=(a.d*b)%mod;return a;}
	public static Mint operator*(Mint a,Mint b){a.d=(a.d*b.d)%mod;return a;}
	public static Mint operator/(Mint a,long b){a.d=(a.d*Mi(b))%mod;return a;}
	public static Mint operator/(Mint a,Mint b){a.d=(a.d*Mi(b.d))%mod;return a;}
	public static bool operator==(Mint a,long b){return (long)a==b;}
	public static bool operator!=(Mint a,long b){return (long)a!=b;}
	public override bool Equals(object obj){return false;}
	public override int GetHashCode(){return 0;}
	public static long Mi(long a){
		a=(a+mod)%mod;
		long b=mod,u=1,v=0;
		while(b>0){
			long t=a/b;
			a-=t*b;(a,b)=(b,a);
			u-=t*v;(u,v)=(v,u);
		}
		u%=mod;
		if(u<0){u+=mod;}
		return u%mod;
	}
}
public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(string a,string b){return Array.ConvertAll((a+Console.ReadLine()+b).Split(),int.Parse);}
	public int[] Ia3(int a){return Array.ConvertAll((Console.ReadLine()+" "+a.ToString()).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(string a,string b){return Array.ConvertAll((a+Console.ReadLine()+b).Split(),long.Parse);}
	public long[] La3(int a){return Array.ConvertAll((Console.ReadLine()+" "+a.ToString()).Split(),long.Parse);}
	public double[] Da2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),double.Parse);}}
	public double[] Da3(string a,string b){return Array.ConvertAll((a+Console.ReadLine()+b).Split(),double.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
	public (T,T) Tp2<T>(){var s=Console.ReadLine().Split();return (Ct<T>(s[0]),Ct<T>(s[1]));}
	public (T,T,T) Tp3<T>(){var s=Console.ReadLine().Split();return (Ct<T>(s[0]),Ct<T>(s[1]),Ct<T>(s[2]));}
	public (T1,T1,T2) Tp3<T1,T2>(){var s=Console.ReadLine().Split();return (Ct<T1>(s[0]),Ct<T1>(s[1]),Ct<T2>(s[2]));}
	private T Ct<T>(string s){return (T)Convert.ChangeType(s,typeof(T));}
}