Description:

bobo has a sequence a_{1},a_{2},…,a_{n}. He is allowed to swap two **adjacent** numbers for no more than k times.

Find the minimum number of inversions after his swaps.

Note: The number of inversions is the number of pair (i,j) where 1≤i<j≤n and a_{i}>a_{j}.

Input:

The input consists of several tests. For each tests:

The first line contains 2 integers n,k (1≤n≤10^{5},0≤k≤10^{9}). The second line contains n integers a_{1},a_{2},…,a_{n} (0≤a_{i}≤10^{9}).

Output:

For each tests:

A single integer denotes the minimum number of inversions.

A single integer denotes the minimum number of inversions.

Sample Input:

3 1 2 2 1 3 0 2 2 1

Sample Output:

1 2

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