KazaQ's Socks

KazaQ wears socks everyday. 

At the beginning, he has nn pairs of socks numbered from 11 to nn in his closets. 

Every morning, he puts on a pair of socks which has the smallest number in the closets. 

Every evening, he puts this pair of socks in the basket. If there are n−1n−1 pairs of socks in the basket now, lazy KazaQ has to wash them. These socks will be put in the closets again in tomorrow evening. 

KazaQ would like to know which pair of socks he should wear on the kk-th day.

Input

The input consists of multiple test cases. (about 20002000) 

For each case, there is a line contains two numbers n,kn,k (2≤n≤109,1≤k≤1018)(2≤n≤109,1≤k≤1018).

Output

For each test case, output " Case #xx: yy" in one line (without quotes), where xxindicates the case number starting from 11 and yy denotes the answer of corresponding case.

Sample Input

3 73 6
4 9
#include <cstdio>#include <algorithm>using namespace std;int main(){    long long t=1,n,k,a[2];    while(~scanf("%lld %lld",&n,&k))    {        a[1]=n-1,a[0]=n;        if(k<=n)        {            printf("Case #%lld: %lld\n",t++,k);        }        else        {            k-=n;            if(k%(n-1)==0)            {                long long num=k/(n-1);                printf("Case #%lld: %lld\n",t++,a[num%2]);            }            else                printf("Case #%lld: %lld\n",t++,k%(n-1));        }    }    return 0;}