The sum is not without variety

Given a sequence of integers (A_1, A_2, ..., A_N).

Your task is to find a subsequence of consecutive numbers, (A_i, A_i+1, ..., A_j), that contains at least (K) distinct numbers. Additionally, you need to maximize the sum (S = A_i + A_i+1 + ...+ A_j).

Input

The first line of input provides the integers (N) and (K) ((1 $\le$ K $\le$ N $\le$ 200,000)).

The second line contains (N) integers (A_1, A_2, ..., A_N) where (|A_i| $\le$ 1,000,000,000).

Output

On the first line, output the maximum possible value of the sum (S). On the second line, output the indices of the first and last elements of the optimal subsequence found. If there are multiple solutions, any valid one will suffice.

If no subsequence meets the criteria, output a single line with the word "IMPOSSIBLE".

Examples