In this problem, you will need to construct a grid with $n$ rows and $n$ columns. Each cell of the grid has an integer in it, where $a_{i,j}$ indicates the integer in the cell located at the $i$-th row and the $j$-th column. Each integer from $1$ to $n^2$ (both inclusive) appears exactly once in the grid.

We say an integer $x$ is a “bingo integer” of this grid, if at least one of the two following conditions is satisfied:

• There is at least one row, where all integers in the cells of that row are less than or equal to $x$.
• There is at least one column, where all integers in the cells of that column are less than or equal to $x$.

It is easy to see that a grid may have multiple bingo integers, however in this problem, we’re only interested in the smallest bingo integer.

Given integers $n$ and $k$, construct a grid with $n$ rows and $n$ columns, such that its smallest bingo integer is exactly $k$.

Input

There are multiple test cases. The first line of the input contains an integer $T$ ($1 \le T \le 50$) indicating the number of test cases. For each test case:

The first and only line contains two integers $n$ and $k$ ($1 \le n \le 50$, $1 \le k \le n^2$).

Output

For each test case:

• If it is possible to construct a grid with $n$ rows and $n$ columns, such that its smallest bingo integer is $k$, first output Yes in one line. Then output $n$ lines, where the $i$-th line contains $n$ integers $a_{i,1}, a_{i,2}, \dots, a_{i,n}$ separated by a space, indicating the integers on the $i$-th row of the grid. Don’t forget that each integer from $1$ to $n^2$ (both inclusive) must appear exactly once in the grid. If there are multiple valid answers, you can output any of them.
• If it is impossible to find an answer, just output No in one line.

Examples

Input 1

4
3 5
4 10
5 2
1 1

Output 1

Yes
4 2 5
7 1 9
8 6 3
Yes
14 9 2 13
1 11 16 8
10 3 7 5
6 15 4 12
No
Yes
1