Imagine you have an infinite 2D plane with Cartesian coordinate system. Initially, all the integral points are painted as white. You are given two integers n, and m. Please paint exactly n integral points to black such that there are exactly m pairs of points which satisfy the following conditions:

1. The two points are colored by different colors.

2. the two points are adjacent. We call two integral points and  being adjacent if and only if . (|v| means the absolute value of v.)

3. The x and y coordinates of all black points are in the range .

The first line contains one integer t () --- the number of test cases.

The only line of each test case contains two integers n and m ().

For each test, if there exists at least one configuration to choose n points to satisfy the conditions given by statement, you should print n+1 line for this test. The first line contains one string "Yes". And the following n lines contain the coordinator of these n points which is colored as black. If there are no solution, please print one line containing only one string "No".

6
5 20
1 2
1 3
1 4
1 5
3 8

Yes
1 1
2 2
3 3
4 4
5 5
No
No
Yes
1 1
No
Yes
1 1
1 2
2 1

In the first test and fourth test, each black point in the sample output is adjacent to exactly 4 white points.
In the sixth test, the second and third black points in the sample output are both adjacent to 3 white points and the forst black point is adjacent to 2 white points.