cf 412 C. Success Rate

原題：
C. Success Rate
time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
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.

中文：
給你四個數x,y,p,q，x表示勝利的次數，y表示比賽總次數。現在問你最少比多少次賽，才能讓x/y等於p/q

#include <bits/stdc++.h>using namespace std;typedef long long ll;const ll inf=9223372036854775807;int main(){    ios::sync_with_stdio(false);    ll x,y,p,q;    int t;    cin>>t;    while(t--)    {        cin>>x>>y>>p>>q;        ll num,den,tot=0;        ll mid,L=0,R=1000000000;        ll ans=inf;        while(R-L>=0)        {            mid=(R+L)/2;            num=mid*p;            den=mid*q;            if(num>=x)            {                tot=num-x;                if(den-tot>=y)                {                    tot+=(den-y-tot);                    ans=tot;                    R=mid-1;                    continue;                }            }            L=mid+1;        }        if(ans==inf)            cout<<-1<<endl;        else            cout<<ans<<endl;    }    return 0;}

解答：

最後x/y一定會變成(n* p)/(n* q)所以，二分n的大小，去構造(n* p)/(n* q)，然後減去x和y即可。
此題應該也可以用純數學方法實現。。。