It's the same type of question as just K above

Title Description

It is known that  nn  It's an integer  x_1,x_2,\cdots,x_nx1​,x2​,⋯,xn​, as well as  11  It's an integer  kk（k<nk<n）. from  nn  Any number of integers  kk  Add the whole numbers , We can get a series of and respectively . For example, when  n=4n=4,k=3k=3,44  The integers are  3,7,12,193,7,12,19  when , All the combinations and their sum can be obtained as ：

3+7+12=223+7+12=22

3+7+19=293+7+19=29

7+12+19=387+12+19=38

3+12+19=343+12+19=34

Now? , Ask you to work out how many kinds of sum are prime numbers .

For example, the above example , There is only one sum of prime numbers ：3+7+19=293+7+19=29.

Input format

The first line is an integer separated by two spaces  n,kn,k（1 \le n \le 201≤n≤20,k<nk<n）.

The second line  nn  It's an integer , Respectively  x_1,x_2,\cdots,x_nx1​,x2​,⋯,xn​（1 \le x_i \le 5\times 10^61≤xi​≤5×106）.

Output format

Output an integer , Indicates the number of species .

I/o sample

Input #1 Copy

4 3
3 7 12 19

Output #1 Copy

1

explain / Tips

【 Title source 】

NOIP 2002 Second question of popularization group

Just summarizing