# 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: 5 seconds

Memory limit: 512 MB

Output limit: 1 MB