Number of primes on an interval

Given n numbers, you are asked to look at all the contiguous sub-arrays of length k and find the segment that has the maximum number of primes in it.

Input

The first line of the input contains two integers n (1 ≤ n ≤ 50 000) and k (1 ≤ k ≤ n).
The next line contains n integers (1 ≤ ).

Output

The program should print the maximum number of primes in a subarray of length k.

Examples

Input
Output
6 3 2 5 10 3 6 7
2
6 3 5 4 2 3 7 1
3
6 2 5 1 6 1 7 4
1
 

Constraints

Time limit: 10 seconds

Memory limit: 512 MB

Output limit: 1 MB

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