Matrix (二分套二分

Given a N × N matrix A, whose element in the i-th row and j-th column A_ij is an number that equals i² + 100000 × i + j² - 100000 × j + i × j, you are to find the M-th smallest element in the matrix.

Input

The first line of input is the number of test case.
For each test case there is only one line contains two integers, N(1 ≤ N ≤ 50,000) and M(1 ≤ M ≤ N × N). There is a blank line before each test case.

Output

For each test case output the answer on a single line.

Sample Input

12

1 1

2 1

2 2

2 3

2 4

3 1

3 2

3 8

3 9

5 1

5 25

5 10

Sample Output

3
-99993
3
12
100007
-199987
-99993
100019
200013
-399969
400031
-99939

 

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
int t;
long long n,k;
long long make(long long i,long long j){
    return i*i+j*j+i*100000-j*100000+i*j;
}
bool erfen(long long m){
    long long cnt=0;
    for(int j=1;j<=n;j++){
        int l=1,r=n,ans=0;
        while(l<=r){//内层二分 
            int i=l+r>>1;
            if(make(i,j)<=m){
                ans=i;
                l=i+1;
            }
            else r=i-1;
        }
        cnt+=ans;
    }
    return cnt>=k;
}
int main(){
    cin>>t;
    for(int w=0;w<t;w++){
        cin>>n>>k;
        long long l=-100000*n;
        long long r=n*n+n*n+100000*n+n*n,ans;
        while(l<=r){//外层二分 
            long long m=l+r>>1;
            if(erfen(m)){ 
                ans=m;
                r=m-1;
            }else l=m+1;
        }
        cout<<ans<<endl;
    }
    return 0;
}