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/JUNE17/mandarin/UNIONSET.pdf">Mandarin</a>, <a target="_blank" 
href="http://www.codechef.com/download/translated/JUNE17/russian/UNIONSET.pdf">Russian</a> and <a target="_blank" 
href="http://www.codechef.com/download/translated/JUNE17/vietnamese/UNIONSET.pdf">Vietnamese</a> as well.</h3>

<p>There are <b>N</b> sets of integers from 1 to <b>K</b> both inclusive. Find out number of pairs of sets whose union contains all the <b>K</b> elements.</p>

<h3>Input</h3>
<p>The first line contains an integer <b>T</b> denotes number of test cases.</p>
<p>The first line of each test case contains two space separated integers <b>N, K</b>.</p>
<p>The each of the next line first contains an integer <b>len</b><sub>i</sub> denoting number of elements in the i-th set, followed by <b>len</b><sub>i</sub> space separated integers in the range [1, <b>K</b>] denoting the elements in the set.</p>

<h3>Output</h3>
<p>For each test case, output a single integer corresponding to the answer.</p>

<h3>Constraints</h3>
<ul>
<li>1 ≤ <b>T</b> ≤ 10</li>
<li>1 ≤ <b>N, K</b> ≤ 2500</li>
<li>1 ≤ <b>len</b><sub>i</sub> ≤ K</li>
<li>Note that a set can't contain repeated elements.</li>
<li>1 ≤ <b>len</b><sub>1</sub> + <b>len</b><sub>2</sub> + .. + <b>len</b><sub><b>N</b></sub> ≤ 10000</li>
</ul>

<h3>Subtasks</h3>
<p><b>Subtask #1</b> (40 points)</p>
<p>
<ul>
<li>1 ≤ <b>T</b> ≤ 10</li>
<li>1 ≤ <b>N, K</b> ≤ 250</li>
<li>1 ≤ <b>len</b><sub>1</sub> + <b>len</b><sub>2</sub> + .. + <b>len</b><sub><b>N</b></sub> ≤ 1000</li>
</ul>
</p>

<p><b>Subtask #2</b> (60 points)</p>
<ul>
<li>original constraints.</li>
</ul>

<h3>Example</h3>
<pre>
<b>Input</b>
3
2 2
1 1
1 1
3 2
2 1 2
2 1 2
2 1 2
3 4
3 1 2 3
4 1 2 3 4
3 2 3 4

<b>Output</b>
0
3
3
</pre>

<h3>Explanation</h3>
<p><b>Example 1</b>. No pair of sets is there with its union = 2.</p>
<p>For <b>example 2 and 3</b>, all the pairs are valid.</p>