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ZOJ Problem Set - 3988
Prime Set

Time Limit: 2 Seconds      Memory Limit: 131072 KB

Given an array of \(n\) integers \(a_1, a_2, \dots, a_n\), we say a set \(\{i, j\}\) is a prime set of the given array, if \(i \ne j\) and \(a_i + a_j\) is prime.

BaoBao has just found an array of \(n\) integers \(a_1, a_2, \dots, a_n\) in his pocket. He would like to select at most \(k\) prime set of that array to maximize the size of the union of the selected sets. That is to say, to maximize \(|\bigcup\limits_{i = 1}^{m}p_i|\) by carefully selecting \(m\) and \(p_1, p_2, \dots, p_m\), where \(m \le k\) and \(p_i\) is a prime set of the given array. Please help BaoBao calculate the maximum size of the union set.

Input

There are multiple test cases. The first line of the input is an integer \(T\), indicating the number of test cases. For each test case:

The first line contains two integers \(n\) and \(k\) (\(1 \le n \le 3\times 10^3\), \(0 \le k \le \frac{n(n-1)}{2}\)), their meanings are described above.

The second line contains \(n\) integers \(a_1, a_2, \dots, a_n\) (\(1 \le a_i \le 10^6\)), indicating the given array.

It's guaranteed that the sum of \(n\) over all test cases will not exceed \(10^4\).

Output

For each test case output one line containing one integer, indicating the maximum size of the union of at most \(k\) prime set of the given array.

Sample Input

4
4 2
2 3 4 5
5 3
3 4 12 3 6
6 3
1 3 6 8 1 1
1 0
1

Sample Output

4
3
6
0

Hint

For the first sample test case, there are 3 prime sets: {1, 2}, {1, 4} and {2, 3}. As \(k = 2\), we can select {1, 4} and {2, 3} to get the largest union set {1, 2, 3, 4} with a size of 4.

For the second sample test case, there are only 2 prime sets: {1, 2} and {2, 4}. As \(k = 3\), we can select both of them to get the largest union set {1, 2, 4} with a size of 3.

For the third sample test case, there are 7 prime sets: {1, 3}, {1, 5}, {1, 6}, {2, 4}, {3, 5}, {3, 6} and {5, 6}. As \(k = 3\), we can select {1, 3}, {2, 4} and {5, 6} to get the largest union set {1, 2, 3, 4, 5, 6} with a size of 6.


Author: WENG, Caizhi
Source: The 2017 China Collegiate Programming Contest, Qinhuangdao Site
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