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Maximum Sum Of M Non-overlapping Subarrays

1. You are given an array(arr) of positive numbers and two numbers M and K. 2. You have to find the maximum sum of M non-overlapping subarrays of size K. 3. The size of the given array(arr) is greater than M*K.

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Maximum Sum Of M Non-overlapping Subarrays

hard

1. You are given an array(arr) of positive numbers and two numbers M and K. 2. You have to find the maximum sum of M non-overlapping subarrays of size K. 3. The size of the given array(arr) is greater than M*K.

Constraints

1 <= N <= 10^3 1 <= arr[i] <= 10^3 M >= 1 K >= 1 N >= M*K

Format

Input

A number N arr1 arr2.. N numbers Two numbers M and K

Output

A number representing maximum sum of M non-overlapping subarrays of size K.

Example

Sample Input

7 2 10 7 18 5 33 0 3 1

Sample Output

61

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