Finding LCM （最小公倍数）

Finding LCM

Time Limit: 2000MS

Memory Limit: 32768KB

64bit IO Format: %lld & %llu

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Description

LCM is an abbreviation used for Least Common Multiple in Mathematics. We say LCM (a, b, c) = L if and only if L is the least integer which is divisible bya, b and c.

You will be given a, b and L. You have to find c such that LCM (a, b, c) = L. If there are several solutions, print the one where c is as small as possible. If there is no solution, report so.

Input

Input starts with an integer T (≤ 325), denoting the number of test cases.

Each case starts with a line containing three integers a b L (1 ≤ a, b ≤ 10⁶, 1 ≤ L ≤ 10¹²).

Output

For each case, print the case number and the minimum possible value of c. If no solution is found, print 'impossible'.

Sample Input

3

3 5 30

209475 6992 77086800

2 6 10

Sample Output

Case 1: 2

Case 2: 1

Case 3: impossible

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;
long long gcd(long long x,long long y)
{
    if(y==0)return x;
    return gcd(y,x%y);
}
int main()
{
    long long a,b,l;
    int n,i,j;
    cin>>n;
    for(i=1; i<=n; i++)
    {
        cin>>a>>b>>l;
        a=a/gcd(a,b)*b;
        if(l%a)
        {
            printf("Case %d: ",i);
            printf("impossible
");
        }
        else
        {
           b=l/a;
           while(gcd(a,b)!=1)
           {
               long long t=gcd(a,b);
               b*=t;
               a/=t;
           }
          printf("Case %d: ",i);
            printf("%lld
",b);
        }
    }
}