C. Painting Grid
time limit per test
1 с
memory limit per test
1024 МБ
input
standard input
output
standard output

Grammy has an $$$n \times m$$$ wall covered by squares. Each small square on the wall is of unit size and should be painted into one color completely. She wants to color the wall into black and white. Grammy likes the concept of diversity, so she decided to make each row look different from all previous rows and also make each column look different from all previous columns. As she was about to paint, she found her paint was just enough: half of white paint and half of black paint, both with an amount to paint exactly $$$\frac{nm}{2}$$$ unit area. Please help Grammy to satisfy her diversity condition using limited paint.

Input

The input contains multiple test cases.

The first line contains a single integer $$$T$$$ ($$$1 \leq T \leq 2000$$$), denoting the number of test cases.

For each test case:

The only line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \leq n,m \leq 1000$$$). It is guaranteed that the sum of $$$n \cdot m$$$ does not exceed $$$10^6$$$.

Output

For each test case, if no solution exists, output "NO". Otherwise, output "YES" followed by $$$n$$$ lines. Each line should contain $$$m$$$ characters. $$$0$$$ denotes a white square and $$$1$$$ denotes a black square in the solution.

Example
Input
5
1 1
2 2
2 4
4 4
5 10
Output
NO
YES
10
01
YES
1100
0110
YES
1100
0110
0000
1111
YES
1111100000
0101010101
0011011001
0000111110
1111000001