You are an experienced Codeforces user. Today you found out that during your activity on Codeforces you have made y submissions, out of which x have been successful. Thus, your current success rate on Codeforces is equal to x / y.

Your favorite rational number in the [0;1] range is p / q. Now you wonder: what is the smallest number of submissions you have to make if you want your success rate to be p / q?

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

Each of the next t lines contains four integers x, y, p and q (0 ≤ x ≤ y ≤ 109; 0 ≤ p ≤ q ≤ 109; y > 0; q > 0).

It is guaranteed that p / q is an irreducible fraction.

Hacks. For hacks, an additional constraint of t ≤ 5 must be met.

Output

For each test case, output a single integer equal to the smallest number of submissions you have to make if you want your success rate to be equal to your favorite rational number, or -1 if this is impossible to achieve.

Example

Input

4
3 10 1 2
7 14 3 8
20 70 2 7
5 6 1 1


Output

4
10
0
-1

Note

In the first example, you have to make 4 successful submissions. Your success rate will be equal to 7 / 14, or 1 / 2.

In the second example, you have to make 2 successful and 8 unsuccessful submissions. Your success rate will be equal to 9 / 24, or 3 / 8.

In the third example, there is no need to make any new submissions. Your success rate is already equal to 20 / 70, or 2 / 7.

In the fourth example, the only unsuccessful submission breaks your hopes of having the success rate equal to 1.
from fractions import gcd

t = int(input())

def ok(x, y, p, q, n):
	np = n * p
	nq = n * q
	a_needed = np - x
	b_needed = nq - y - a_needed
	if a_needed < 0 or b_needed < 0:
		return False
	return True

while t > 0:
	t -= 1
	x, y, p, q = [int(x) for x in input().split()]
	low = 0
	high = int(1e36)
	poss = -1
	while high >= low:
		mid = (high + low) // 2
		if ok(x, y, p, q, mid):
			poss = mid
			high = mid - 1
		else:
			low = mid + 1
	if poss == -1:
		print(poss)
	else:
		a_needed = poss * p - x
		b_needed = poss * q - y - a_needed
		print (a_needed + b_needed)
