Sajin gives you integers , and gives you a task:

Find any 01-matrix with rows and columns where sum of each row and each column is odd. Among all of elements, there are exactly elements have value and elements have value .

输入描述:

Each test contains multiple test cases. The first line contains the number of test cases  (). Description of the test cases follows.

Each test case has  integers  () - the height and width of the 01-matrix, the number of elements with value , respectively.

It is guaranteed that the sum of  over all test cases does not exceed .

输出描述:

If the matrix is not existed, print a single line containing "No".

Otherwise print a line containing "Yes" and the next each  line print  integers , which means . 

If there are multiple answers, print any.

You can print letters in any case (upper or lower).

4
2 2 1
2 2 2
3 3 3
4 4 10

No
Yes
1 2
2 1
Yes
1 3
2 2
3 1
Yes
1 3
1 2
1 1
2 3
2 2
2 1
3 4
3 3
3 2
4 1