Problem B

Statement
Copy Copied
Description:
Even in kindergarten, Sasha liked a girl. Therefore, he wanted to give her a drawing and attract her attention.

As a drawing, he decided to draw a square grid of size $$$n \times n$$$, in which some cells are colored. But coloring the cells is difficult, so he wants to color as few cells as possible. But at the same time, he wants at least $$$k$$$ diagonals to have at least one colored cell. Note that the square grid of size $$$n \times n$$$ has a total of $$$4n - 2$$$ diagonals.

Help little Sasha to make the girl fall in love with him and tell him the minimum number of cells he needs to color.

Input Format:
Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$2 \leq n \leq 10^8$$$, $$$1 \leq k \leq 4n - 2$$$) — the size of the square grid and the minimum number of diagonals in which there should be at least one colored cell.

Output Format:
For each test case, output a single integer — the minimum number of cells that need to be colored.

Note:
In the pictures below, the colored cells are marked in black, and all diagonals are marked in purple.

In the first test case, you can color $$$2$$$ cells so that $$$4$$$ diagonals contain at least one colored cell:

In the third test case, you can color $$$6$$$ cells so that all $$$10$$$ diagonals contain at least one colored cell: