import bisect
import copy
import decimal
import fractions
import heapq
import itertools
import math
import random
import sys
import time
from collections import Counter,deque,defaultdict
from functools import lru_cache,reduce
from heapq import heappush,heappop,heapify,heappushpop,_heappop_max,_heapify_max
def _heappush_max(heap,item):
    heap.append(item)
    heapq._siftdown_max(heap, 0, len(heap)-1)
def _heappushpop_max(heap, item):
    if heap and item < heap[0]:
        item, heap[0] = heap[0], item
        heapq._siftup_max(heap, 0)
    return item
from math import gcd as GCD
read=sys.stdin.read
readline=sys.stdin.readline
readlines=sys.stdin.readlines
write=sys.stdout.write
#import pypyjit
#pypyjit.set_param('max_unroll_recursion=-1')
#sys.set_int_max_str_digits(10**9)

def Extended_Euclid(n,m):
    stack=[]
    while m:
        stack.append((n,m))
        n,m=m,n%m
    if n>=0:
        x,y=1,0
    else:
        x,y=-1,0
    for i in range(len(stack)-1,-1,-1):
        n,m=stack[i]
        x,y=y,x-(n//m)*y
    return x,y

T=int(readline())
mod=10**9+7
for t in range(T):
    N,K,H,Y=map(int,readline().split())
    N,K,H=sorted([N,K,H])
    ans=0
    g=GCD(N,K)
    N//=g
    K//=g
    for h in range(Y//H+1):
        YY=Y-h*H
        if YY%g:
            continue
        n,k=Extended_Euclid(N,K)
        n*=YY
        k*=YY
        ans+=max(0,k//N+1-(-n+K-1)//K)
    print(ans)