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K-Concatenation Maximum Sum

Given an integer array arr and an integer k, modify the array by repeating it k times.

Given an integer array arr and an integer k, modify the array by repeating it k times.

For example, if arr = [1, 2] and k = 3 then the modified array will be [1, 2, 1, 2, 1, 2].

Return the maximum sub-array sum in the modified array. Note that the length of the sub-array can be 0 and its sum in that case is 0.

As the answer can be very large, return the answer modulo 10^9 + 7.

K-Concatenation Maximum Sum diagram

Example 1

Input: arr = [1,2], k = 3

Output: 9

Example 2

Input: arr = [1,-2,1], k = 5

Output: 2

Example 3

Input: arr = [-1,-2], k = 7

Output: 0

Constraints

  • 1 <= arr.length <= 10^5
  • 1 <= k <= 10^5
  • -10^4 <= arr[i] <= 10^4

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