E. Jamal Fofo Two of a Kind Length of a Path Out of Your Mind
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

It is a well-known fact in the problemsetting room: Fofo absolutely despises trees, and Jamal harbors an intense hatred for grids. Naturally, the room was left in stunned silence when Fofo, with a mischievous grin, unexpectedly proposed a tree problem.

Before the ink could even dry, Jamal narrowed his eyes and hit him with a swift, merciless $$$\texttt{3rr}$$$.

"Project it onto a grid," Jamal demanded.

After a fierce clash of wills, a compromise was born. What lies before you is the ultimate cocktail of Jamal and Fofo's $$$\texttt{7as7aseh}$$$—a grid problem haunted by the ghost of a tree.

Consider an $$$n \times m$$$ grid. A path is a sequence of cells moving exclusively down or to the right, starting and ending at distinct positions. The length of a path is the total number of cells it traverses.

Your challenge is to survive their $$$\texttt{7as7aseh}$$$ by filling the grid with positive integers such that it satisfies one core property: for every path of length $$$L$$$, at least two cells along that path must contain values divisible by $$$L$$$.

If their combined trap is too strong and no such valid grid exists, report that it is impossible.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

Each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n,m \le 300$$$) — the number of rows and columns.

It is guaranteed that the sum of $$$n \cdot m$$$ over all test cases does not exceed $$$90000$$$.

Output

For each test case, print NO if it is impossible to construct a valid grid.

Otherwise, print YES, followed by $$$n$$$ lines. Each of these lines must contain $$$m$$$ integers, the values in the grid. Every value must be between $$$1$$$ and $$$10^9$$$, inclusive.

You may print YES and NO in any case. If there are several valid grids, print any of them.

Example
Input
3
1 1
1 3
2 2
Output
YES
1000000000
YES
6 6 6
YES
12 6
6 12
Note

The provided sample illustrates just one possible valid configuration.

In the first test case, there does not exist any path starting and ending at distinct positions. Hence, any grid works.