Given an array of

`n`

integers, you are asked to calculate the number of subarrays that have at most `k`

distinct characters. Input

The first line of the input contains two integers

`n`

and `k`

(1 ≤ k ≤ n ≤ ).The next line contains

`n`

space-separated integers (1 ≤ ≤ ). Output

The program should print the number of subarrays that have at most

`k`

distinct values. Examples

Input | Output |

5 2
2 3 4 2 2 | 10 |

Explanation

`2`

, `3`

, `4`

, `2`

, `2`

, `2 3`

, `3 4`

, `4 2`

, `2 2`

, `4 2 2`