Marjar Cola（zoj 3948）

Marjar Cola

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Time Limit: 1 Second      Memory Limit: 65536 KB

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Marjar Cola is on sale now! In order to attract more customers, Edward, the boss of Marjar Company, decides to launch a promotion: If a customer returns x empty cola bottles or y cola bottle caps to the company, he can get a full bottle of Marjar Cola for free!

Now, Alice has a empty cola bottles and b cola bottle caps, and she wants to drink as many bottles of cola as possible. Do you know how many full bottles of Marjar Cola she can drink?

Note that a bottle of cola consists of one cola bottle and one bottle cap.

Input

There are multiple test cases. The first line of input contains an integer T (1 ≤ T ≤ 100), indicating the number of test cases. For each test case:

The first and only line contains four integers x, y, a, b (1 ≤ x, y, a, b ≤ 100). Their meanings are described above.

Output

For each test case, print one line containing one integer, indicating the number of bottles of cola Alice can drink. If Alice can drink an infinite number of bottles of cola, print "INF" (without the quotes) instead.

Sample Input

2
1 3 1 1
4 3 6 4

Sample Output

INF
4

Hint

For the second test case, Alice has 6 empty bottles and 4 bottle caps in hand. She can return 4 bottles and 3 caps to the company to get 2 full bottles of cola. Then she will have 4 empty bottles and 3 caps in hand. She can return them to the company again and get another 2 full bottles of cola. This time she has 2 bottles and 2 caps in hand, but they are not enough to make the exchange. So the answer is 4.

题意：可以用x个可乐瓶或y个盖子换一瓶新的可乐（一瓶可乐包括1个瓶子和1个盖子），现在有a个可乐瓶和b个盖子，问最多可以换多少瓶可乐。（若可以换无穷多的可乐则输出INF）。

思路：主体用一个循环即可，关键是判断INF的情况，有2种：

1. 若x、y中有一个为1，则ans=INF;

2. 若x=y=2，且a>=2或b>=2，则ans=INF;

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <queue>
#include <vector>
#include <algorithm>
using namespace std;

int x,y,a,b;

int main()
{
    int T;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d%d%d%d",&x,&y,&a,&b);
        
        if(x==1&&a>=1)
        {
            printf("INF\n");
            continue;
        }
        
        if(y==1&&b>=1)
        {
            printf("INF\n");
            continue;
        }
        
        if(x==2&&y==2)
        {
            if(a>=2||b>=2)
            {
                printf("INF\n");
                continue;
            }
        }
        
        int ans=0;
        while(true)
        {
            int num=a/x+b/y;
            if(num==0)
                break;
            a=a-(a/x)*x+num;
            b=b-(b/y)*y+num;
            ans+=num;
        }
        printf("%d\n",ans);
    }
}