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Codeforces 807C - Success Rate(二分枚举)

热度:112   发布时间:2023-11-23 06:27:53.0

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;}elsel=mid+1;}if(ans==-1)printf("-1\n");elseprintf("%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 xyp 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.

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