Maximum Sum Segments

You are given an array of n integers and an integer w representing the length of a segment. Your task is to determine the maximum sum of any segment consisting of w consecutive elements and count the number of segments that achieve this sum.

Formally, let \(a_1,a_2,\dots,a_n\) be the array and define the segment sum \(S_i = \sum_{j=i}^{i+w-1}a_j\) for \(1 \le i \le n-w+1\). You need to find \(M = \max_{1\le i \le n-w+1}{S_i}\) and the number of indices \(i\) such that \(S_i = M\).

If w is 0 or if the array is empty, output 0 0.

inputFormat

The input consists of two lines:

• The first line contains two space-separated integers: n (the number of elements in the array) and w (the length of the segment).
• The second line contains n space-separated integers representing the array elements.

You can assume that the input is valid and n is at least equal to w when w > 0.

outputFormat

Output a single line containing two space-separated integers: the maximum sum of any segment of length w and the number of segments that achieve this maximum sum.

## sample

10 3
1 2 3 4 5 6 7 8 9 10

27 1

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