Solve the programming task below in a Python markdown code block.
Read problems statements in mandarin chinese, russian and vietnamese as well. 

Chef Ada loves trees, she thinks that the beauty of a tree is determined by the distance between its center and centroid. If the tree has multiple centers or centroids, then the beauty is the maximum among every possible pair.

As a reward for her delicious dishes (and awesome coding skills), CodeChef is going to give a present to Chef Ada, and of course it must be a tree! But not any tree, we want to give her one with n nodes, and beauty b. Help find such a tree.

------ Input ------ 

The first line of input contains one number T, the number of test cases.

Each test case contains two integers n and b, the desired number of vertices and beauty.

------ Output ------ 

For each test case, if no tree satisfies the conditions print "NO" in a new line.

Otherwise, print "YES" in a new line and describe any valid tree. Print n-1 more lines, each with two integers u_{i}, v_{i} (1 ≤ u_{i}, v_{i} ≤ n) denoting the indices of the vertices connected by an edge in the tree.

------ Constraints ------ 

1 ≤ T ≤ 10^{4}
2 ≤ n ≤ 100
0 ≤ b ≤ n-1

------ Notes ------ 

A vertex u is a centroid if after removing u from the tree, the size of any of the resulting connected components is at most n/2.

Lef f(x) be the greatest distance from u to any other vertex of the tree. A vertex u is a center if f(u) ≤ f(v)  for any other vertex v.

----- Sample Input 1 ------ 
1
4 0
----- Sample Output 1 ------ 
YES
1 2
1 3
1 4
----- explanation 1 ------ 

Vertex 1 is the center and centroid of the tree.