Vitaly503 is given a checkered board with a side of $$$n$$$ and $$$k$$$ chips. He realized that all these $$$k$$$ chips need to be placed on the cells of the board (no more than one chip can be placed on a single cell).

Let's denote the cell in the $$$i$$$-th row and $$$j$$$-th column as $$$(i ,j)$$$. A diagonal is the set of cells for which the value $$$i + j$$$ is the same. For example, cells $$$(3, 1)$$$, $$$(2, 2)$$$, and $$$(1, 3)$$$ lie on the same diagonal, but $$$(1, 2)$$$ and $$$(2, 3)$$$ do not. A diagonal is called occupied if it contains at least one chip.

Determine what is the minimum possible number of occupied diagonals among all placements of $$$k$$$ chips.

Input

Each test consists of several sets of input data. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 500$$$) — the number of sets of input data. Then follow the descriptions of the sets of input data.

The only line of each set of input data contains two integers $$$n$$$, $$$k$$$ ($$$1 \le n \le 100, 0 \le k \le n^2$$$) — the side of the checkered board and the number of available chips, respectively.

Output

For each set of input data, output a single integer — the minimum number of occupied diagonals with at least one chip that he can get after placing all $$$k$$$ chips.

Note

In the first test case, there are no chips, so 0 diagonals will be occupied. In the second test case, both chips can be placed on diagonal $$$(2, 1), (1, 2)$$$, so the answer is 1. In the third test case, 3 chips can't be placed on one diagonal, but placing them on $$$(1, 2), (2, 1), (1, 1)$$$ makes 2 diagonals occupied. In the 7th test case, chips will occupy all 5 diagonals in any valid placing.

Diagonals

Examples