Problem Statement

You are given positive integers $N$ and $K$.

There is a complete bipartite graph $G$ with $N$ vertices $l_1, l_2, \ldots, l_N$ on the left and $N$ vertices $r_1, r_2, \ldots, r_N$ on the right. It has $N^2$ edges; for each $(i, j)\ (1\leq i\leq N, 1\leq j\leq N)$, there is one undirected edge between vertices $l_i$ and $r_j$.

Determine whether there exists a way to write an integer between $1$ and $N^2$, inclusive, on each edge of $G$ (where the $N^2$ integers written are all distinct) such that the answer to the following problem is $K$, and if such a way exists, find one.

Among all walks on graph $G$, we call a walk good if the sequence of numbers written on the edges traversed, in the order they are traversed, is strictly increasing.

Find the maximum number of edges contained in a good walk.

$T$ test cases are given; solve each of them.

What is a walk? A walk on graph $G$ is a sequence of $k$ vertices and $k-1$ edges alternately arranged, $(v_1 ​ ,e_1 ​ ,v_2 ​ ,\ldots,v_{k−1} ​ ,e_{k−1} ​ ,v_k)$ (where $k$ is a positive integer), such that edge $e_i$ connects vertices $v_i$ and $v_{i+1}$.

Constraints

• $1\leq T\leq 3000$
• $1\leq N\leq 700$
• $1\leq K\leq N^2$
• The sum of $N^2$ in each input is at most $5\times 10^5$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
\mathrm{case}_1
\mathrm{case}_2
\vdots
\mathrm{case}_T

Each test case is given in the following format:

N K

Output

Output the answers for $\mathrm{case}_1,\mathrm{case}_2,\ldots,\mathrm{case}_T$ in this order in the following format.

If no valid way of writing exists, output No.

If a valid way exists, letting $A_{i,j}$ be the integer written on the edge connecting vertices $l_i$ and $r_j$,

Yes
A_{1,1} A_{1,2} \ldots A_{1,N}
A_{2,1} A_{2,2} \ldots A_{2,N}
\vdots
A_{N,1} A_{N,2} \ldots A_{N,N}

output as above. $(A_{1,1},\ldots,A_{1,N},A_{2,1},\ldots,A_{2,N},\ldots,A_{N,1},\ldots,A_{N,N})$ must be a permutation of $(1,2,\ldots,N^2)$.

If multiple solutions exist, any of them will be accepted.