Codeforces 807C - Success Rate(二分枚舉)

題意：

給你T組數據，每組有x,y,p,q四個數，x/y是你當前提交正確率，讓你求出最少需要再提交幾次可以達到目標正確率p/q;

思路：

假設提交B次，正確A次，那麼可以得到（x+A）/(y+B)=p/q,可以推出x+A=k*p,y+B=k*q.那麼A=k*p-x，B=K*q-y;

這樣我們只需要二分枚舉k，判斷A,B是否滿足（0<=A<=B）即可。

代碼：

#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;
}

題目：

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.