Complex Market Analysis

Description:

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10\,000$$$). Description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$e$$$ $$$(1 \le e \le n \le 2 \cdot 10^5)$$$, the number of items in the array and number $$$e$$$, respectively.

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

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output:

For each test case output the answer in the following format:

Output one line containing the number of pairs of numbers $$$(i, k)$$$ which satisfy the conditions.

Sample Input:

6
7 3
10 2 1 3 1 19 3
3 2
1 13 1
9 3
2 4 2 1 1 1 1 4 2
3 1
1 1 1
4 1
1 2 1 1
2 2
1 2

Sample Output:

2
0
4
0
5
0

Note:

In the first example test case two pairs satisfy the conditions:

1. $$$i = 2, k = 1$$$, for which the product is: $$$a_{2} \cdot a_{5} = 2$$$ which is a prime number.
2. $$$i = 3, k = 1$$$, for which the product is: $$$a_{3} \cdot a_{6} = 19$$$ which is a prime number.

In the second example test case there are no pairs that satisfy the conditions.

In the third example test case four pairs satisfy the conditions:

1. $$$i = 1, k = 1$$$, for which the product is: $$$a_{1} \cdot a_{4} = 2$$$ which is a prime number.
2. $$$i = 1, k = 2$$$, for which the product is: $$$a_{1} \cdot a_{4} \cdot a_{7} = 2$$$ which is a prime number.
3. $$$i = 3, k = 1$$$, for which the product is: $$$a_{3} \cdot a_{6} = 2$$$ which is a prime number.
4. $$$i = 6, k = 1$$$, for which the product is: $$$a_{6} \cdot a_{9} = 2$$$ which is a prime number.

In the fourth example test case there are no pairs that satisfy the conditions.

In the fifth example test case five pairs satisfy the conditions:

1. $$$i = 1, k = 1$$$, for which the product is: $$$a_{1} \cdot a_{2} = 2$$$ which is a prime number.
2. $$$i = 1, k = 2$$$, for which the product is: $$$a_{1} \cdot a_{2} \cdot a_{3} = 2$$$ which is a prime number.
3. $$$i = 1, k = 3$$$, for which the product is: $$$a_{1} \cdot a_{2} \cdot a_{3} \cdot a_{4} = 2$$$ which is a prime number.
4. $$$i = 2, k = 1$$$, for which the product is: $$$a_{2} \cdot a_{3} = 2$$$ which is a prime number.
5. $$$i = 2, k = 2$$$, for which the product is: $$$a_{2} \cdot a_{3} \cdot a_{4} = 2$$$ which is a prime number.

In the sixth example test case there are no pairs that satisfy the conditions.