Codeforces 807C - Success Rate(二分枚举)

题意：

给你T组数据，每组有x,y,p,q四个数，x/y是你当前提交正确率，让你求出最少需要再提交几次可以达到目标正确率p/q;

思路：

假设提交B次，正确A次，那么可以得到（x+A）/(y+B)=p/q,可以推出x+A=k*p,y+B=k*q.那么A=k*p-x，B=K*q-y;

这样我们只需要二分枚举k，判断A,B是否满足（0<=A<=B）即可。

代码：

#include<bits/stdc++.h> using namespace std; typedef long long ll; const int maxn=1e6+10; const int mod=1e9; int main() { int t; scanf("%d",&t); while(t--) { ll x,y,p,q; ll ans=-1; scanf("%lld%lld%lld%lld",&x,&y,&p,&q); ll l=0,r=1000000000; while(r-l>=0) { ll mid,b,d; mid=(l+r)/2; b=mid*p-x; d=mid*q-y; if(b>=0&&d>=0&&b<=d) { ans=mid; r=mid-1; } else l=mid+1; } if(ans==-1) printf("-1\n"); else printf("%lld\n",ans*q-y); } return 0; }

题目：

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.