Dots and lines

Vasja and Pete play the following game. Vasja draws on the plane of N points and says the number of M. Peter has to answer whether you can combine these N points with M lines, so that:

1. Each line connects exactly two points.

2. No line is not connecting the dots with itself.

3. For any pair of points there is no more than one connecting their lines.

4. There exist two points A and B, that can not get from A along the drawn lines to B (for each line can go in any direction).

When Peter answers correctly, he wins, otherwise Vasja wins.

Your task - to write a program that helps Pete always win.

Input

The first line of the input file is written the number of K - number of tests in the input file (1 ≤ K ≤ 1000). The following K lines contain the number N (1 ≤ N ≤ 10^9) and M (0 ≤ M ≤ 10^9).

Output

For each of the K tests on a separate line write down the correct answer to the question Vasja, a string "Yes" (if yes) or "No" (if the answer is no.)

Examples