# lcm(a,b) ごとに繰り返す
# 0, 3, 6, 9, 12, 15,
# 0,   5,    10,   15,
# 3/2/1/3/1/2/3

# 0, 3, 6, 9, 12, 15, 18, 21
# 0,     7,      14,      21
#   3/3/1/2/3/2/1/3/3

# 0, 5, 10, 15, 20, 25, 30, 35
# 0,  7,  14,    21,   28,  35
# 5 / 2 / 3 / 4 / 1 / 5 / 1 / 4 / 3 / 2 / 5
# 1-4 ... 2 個ずつ 5 ... 3個


# 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
# 0,     11,     22,      33,      44,      55
# 5 / 5 / 1 / 4 / 5 / 2 / 3 / 5 / 3 / 2 / 5 / 4 / 1 / 5 / 5
# 1-4... 2 個ずつ, 5 ... (差+1) 個

# 0, 2, 4, 6
# 0,  3,   6
# 2/1/1/2

import os
import sys
from io import BytesIO, IOBase

BUFSIZE = 8192


class FastIO(IOBase):
	newlines = 0
	
	def __init__(self, file):
		self._fd = file.fileno()
		self.buffer = BytesIO()
		self.writable = "x" in file.mode or "r" not in file.mode
		self.write = self.buffer.write if self.writable else None
	
	def read(self):
		while True:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			if not b:
				break
			ptr = self.buffer.tell()
			self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
		self.newlines = 0
		return self.buffer.read()
	
	def readline(self):
		while self.newlines == 0:
			b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
			self.newlines = b.count(b"\n")+(not b)
			ptr = self.buffer.tell()
			self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
		self.newlines -= 1
		return self.buffer.readline()
	
	def flush(self):
		if self.writable:
			os.write(self._fd, self.buffer.getvalue())
			self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
	def __init__(self, file):
		self.buffer = FastIO(file)
		self.flush = self.buffer.flush
		self.writable = self.buffer.writable
		self.write = lambda s:self.buffer.write(s.encode("ascii"))
		self.read = lambda:self.buffer.read().decode("ascii")
		self.readline = lambda:self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda:sys.stdin.readline().rstrip("\r\n")

from math import gcd

def xgcd(a,b):
    prevx, nextx = 1, 0
    prevy, nexty = 0, 1
    while b:
        quotient = a//b
        nextx, prevx = prevx - quotient * nextx, nextx
        nexty, prevy = prevy - quotient * nexty, nexty
        a, b = b, a % b
    return prevx, prevy

def naive(m,a,b,k):
	t = 0
	ans = 0
	for i in range(1, m+1):
		if i%a == 0 or i%b == 0:
			if i-t==k:
				ans += 1
			t = i
	return ans

def fast(m,a,b,k):
	ret = 0
	if k == a:
		tmp = (m+a-1)//a
		ret += tmp - tmp*a//b
		return ret
	else:
		x,y = xgcd(a,b)
		x*=k; y*=k

		r1 = x*a%(a*b)
		r2 = -y*b%(a*b)
		if r1 < r2:
			if r2 <= m:
				ret += 1
		else:
			if r1 <= m:
				ret += 1
		
		r1 = -x*a%(a*b)
		r2 = y*b%(a*b)
		if r1 < r2:
			if r2 <= m:
				ret += 1
		else:
			if r1 <= m:
				ret += 1
		
	return ret


T = int(input())
for _ in range(T):
	m,a,b,k = map(int,input().split())
	#print(naive(m,a,b,k))
	if a>b: a,b = b,a
	g = gcd(a,b)
	if k % g != 0:
		print(0)
		continue
	a//=g
	b//=g
	m//=g
	k//=g
	# gcd(a,b) == 1
	l = a*b
	if k>a:
		print(0)
		continue
	if a==1:
		print(max(0,m-1))
		continue
	r = m//l
	ans = 0
	m %= l
	if k==a:
		ans = (b-a+1)*r-1
	elif k<a:
		ans = 2*r
	ans += fast(m,a,b,k)
	print(max(0,ans))