Description

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.

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

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

Source

, windy7926778