github.com/captn3m0/codechef.git

---
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---
<span class="solution-visible-txt">All submissions for this problem are available.</span><h3>Read problems statements in <a target="_blank" href="http://www.codechef.com/download/translated/COOK83/mandarin/CENTREE.pdf">mandarin chinese</a>, <a target="_blank" href="http://www.codechef.com/download/translated/COOK83/russian/CENTREE.pdf">russian</a> and <a target="_blank" href="http://www.codechef.com/download/translated/COOK83/vietnamese/CENTREE.pdf">vietnamese</a> as well.</h3>

<p>
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.
</p>
<p>
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 <b>n</b> nodes, and beauty <b>b</b>. Help find such a tree.
</p>

<h3>Input</h3>
<p>
The first line of input contains one number <b>T</b>, the number of test cases.
</p>
<p>
Each test case contains two integers <b>n</b> and <b>b</b>, the desired number of vertices and beauty.
</p>
<h3>Output</h3>
<p>
For each test case, if no tree satisfies the conditions print "NO" in a new line.
</p>
<p>
Otherwise, print "YES" in a new line and describe any valid tree. Print <b>n-1</b> more lines, each with two integers <b>u<sub>i</sub></b>, <b>v<sub>i</sub></b> (1 ≤ <b>u<sub>i</sub></b>, <b>v<sub>i</sub></b> ≤ <b>n</b>) denoting the indices of the vertices connected by an edge in the tree.
</p>

<h3>Constraints</h3>

<li>1 ≤ <b>T</b> ≤ 10<sup>4</sup></li>
<li>2 ≤ <b>n</b> ≤ 100</li>
<li>0 ≤ <b>b</b> ≤ n-1</li>

<h3>Notes</h3>
<p>
A vertex <b>u</b> is a centroid if after removing <b>u</b> from the tree, the size of any of the resulting connected components is at most <b>n/2</b>.
</p>
<p>
Lef <b>f(x)</b> be the greatest distance from <b>u</b> to any other vertex of the tree. A vertex <b>u</b> is a center if <b>f(u) ≤ f(v) </b> for any other vertex <b>v</b>.
</p>

<h3>Example</h3>
<pre>
<b>Input:</b>
1
4 0

<b>Output:</b>
YES
1 2
1 3
1 4
</pre>
<h3>Explanation</h3>
<p>
Vertex 1 is the center and centroid of the tree.
</p>