A group of N Internet Service Provider companies (ISPs) use a private communication channel that has a maximum capacity of C traffic units per second. Each company transfers T traffic units per second through the channel and gets a profit that is directly proportional to the factor T(C - T*N). The problem is to compute the smallest value of T that maximizes the total profit the N ISPs can get from using the channel. Notice that N, C, T, and the optimal T are integer numbers.
Input
Input starts with an integer T (≤ 20), denoting the number of test cases.
Each case starts with a line containing two integers N and C (0 ≤ N, C ≤ 109).
Output
For each case, print the case number and the minimum possible value of T that maximizes the total profit. The result should be an integer.
Sample Input
6
1 0
0 1
4 3
2 8
3 27
25 1000000000
Sample Output
Case 1: 0
Case 2: 0
Case 3: 0
Case 4: 2
Case 5: 4
Case 6: 20000000
#include<iostream>
#include<cstdio>
#include<algorithm>
#define ll long long
using namespace std;
int t;
int main()
{
scanf("%d",&t);
int w=0;
while(t--)
{w++;
ll n,c;
scanf("%lld%lld",&n,&c);
if(n==0)
{printf("Case %d: 0\n",w);
continue;
}
ll a=c/(2*n);
ll b=a+1;
if(a*(c-a*n)>=b*(c-b*n))
printf("Case %d: %lld\n",w,a);
else
printf("Case %d: %lld\n",w,b);
}
return 0;
}