Description

Given n integers b₁, b₂, ..., bₙ

and an integer k (k < n).

Select any k integers from the n integers and add them together to obtain a series of sums.

For example, when n=4, k=3, and the 4 integers are 3, 7, 12, and 19, all possible combinations and their sums are:
3 + 7 + 12 = 22　　3 + 7 + 19 = 29　　7 + 12 + 19 = 38　　3 + 12 + 19 = 34.
Now, you are required to calculate how many of these sums are prime numbers.

In the example above, there is only one sum that is a prime number: 3 + 7 + 19 = 29.

Input Format

The first line contains two integers:n, k (1 ≤ n ≤ 20, k < n)

The second line contains n integers: x₁, x₂, ..., xₙ (1 ≤ xᵢ ≤ 5,000,000)

Output Format

An integer (the number of valid schemes).

```input1 4 3 3 7 12 19 ``` ```output1 1 ``` ## 译文

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