Codeforces Round #412 C. Success Rate

Posted 2020-09-20 starry

Success Rate

 

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.

 

由题可知，要满足（x+a）/（y+b） == np/nq  ，所以（x+a）=np ， （y+b）=nq。由于0 <= a <= b,所以n>=x/p,x>=(y-x)/(q-p) 向上取整求满足条件的最小n值，

就可得答案是b=nq-y；

p==q 和p==0特判下

 

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 #define ll long long
 4 ll x, y, q, p;
 5 int main(){
 6     int t;
 7     cin >> t;
 8     while(t--){
 9         cin >> x >> y >> p >> q;
10         if(q == p){
11             printf("%d\n",(x==y)?0:-1);
12             continue;
13         }
14         if(p == 0){
15             printf("%d\n",(x==0)?0:-1);
16             continue;
17         }
18         ll GCD = __gcd(q,p);
19         q/=GCD; p/=GCD;
20         ll n = max(ceil(x*1.0/p),ceil((y-x)*1.0/(q-p)));
21         printf("%lld\n",n*q-y);
22     }
23     return 0;
24 }