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.
def solve(x, y, p, q):
	if p == 0 and x == 0:
		return 0;
	if p == 0 and x > 0:
		return -1
	if p == 1 and q == 1 and x < y:
		return -1
	a = max(x // p, y // q)
	pp = a * p
	qq = a * q
	while pp < x or qq < y:
		a = a + 1
		pp = pp + p
		qq = qq + q
	if pp - x > qq - y:
		d = (pp - x) - (qq - y)
		dd = q - p
		it = d // dd
		a = a + it
		pp = p * a
		qq = q * a
		while pp - x > qq - y:
			a = a + 1
			pp = pp + p
			qq = qq + q
	return qq - y

TC = input()
for tc in range(0, TC):
	x, y, p, q = map(int, raw_input().split())
	print solve(x, y, p, q)
