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You are given an array $a$ of length $n$ and an integer $c$ .

The value of some array $b$ of length $k$ is the sum of its elements except for the  smallest. For example, the value of the array $[3,1,6,5,2]$ with $c=2$ is $3+6+5=14$ .

Among all possible partitions of $a$ into contiguous subarrays output the smallest possible sum of the values of these subarrays.

The first line contains integers $n$ and $c$ ( $1<=n,c<=100000$ ).

The second line contains $n$ integers $a_{i}$ ( $1<=a_{i}<=10^{9}$ ) — elements of $a$ .

Output a single integer — the smallest possible sum of values of these subarrays of some partition of $a$ .