杭电_ACM_Wolf and Rabbit

Problem Description

There is a hill with n holes around. The holes are signed from 0 to n-1.



A rabbit must hide in one of the holes. A wolf searches the rabbit in anticlockwise order. The first hole he get into is the one signed with 0. Then he will get into the hole every m holes. For example, m=2 and n=6, the wolf will get into the holes which are signed 0,2,4,0. If the rabbit hides in the hole which signed 1,3 or 5, she will survive. So we call these holes the safe holes.

 

Input

The input starts with a positive integer P which indicates the number of test cases. Then on the following P lines,each line consists 2 positive integer m and n(0<m,n<2147483648).

 

Output

            For each input m n, if safe holes exist, you should output "YES", else output "NO" in a single line.

 

Sample Input

2
1 2
2 2

 

Sample Output

NO
YES

#include <stdio.h>
//get the greatest common divisor
int gcd(int a, int b)
{
    int r;
    while (b)
    {
        r = a % b;
        a = b;
        b = r;
    }
    return a;
}
int main()
{
    int N, m, n;
    scanf("%d", &N);
    while(N--)
    {
        scanf("%d %d", &n, &m);
        if(gcd(n, m) == 1)
            printf("NO\n");
        else
            printf("YES\n");
    }
    return 0;
}

The reason why we can judge by greatest common divisor(gcd):

Condition:

firstly, r is the gcd of a, b and a is bigger than b, t is the lowest common multiple(lcm) of a, b

then you can get 

r = gcd(a, b)

t = a * b / r

secondly, the wolf find the t hold, the wolf will stop, because it's will be circulatory.

-------------------------

Question

the question is to find 0 < x < t / a and 0 < y < t / b to satisfy the equality

ax + r = by

for the equality, you will find (by - ax) / r is a integer, so you can find x, y making (by - ax) / r = 1

------------------------

Conclusion

"ax + r = by" means the r hole will be found, in other words, the gcd will be found.

so, if gcd is equal to 1, it means all holes will be found. if gcd is equal to other number, it means there are safe holes.