Optimizing Resource Allocation

Choose a contiguous window of length exactly k whose elements are pairwise distinct, maximizing the sum of its elements. If there is no valid window, output −1.

输入格式

The first line contains n k, and the second line contains n integers; when n=0, the second line may be empty. This site adds 0≤n≤200000, 1≤k≤200000, and −10^9≤a[i]≤10^9; k may be greater than n, and negative numbers are not excluded.

输出格式

Output a single integer, the answer.

样例 1

输入：

6 3
1 2 3 7 3 5

输出：

15

样例 2

输入：

3 2
-5 -2 -3

输出：

-5

样例 3

输入：

2 2
1 1

输出：

-1

样例说明

The outputs of the three public examples are, in order: 15; -5; -1. Verified by independent enumeration or direct simulation.