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#### MinMaxDivision

Divide array A into K blocks and minimize the largest sum of any block.

You are given integers K, M and a non-empty array A consisting of N integers. Every element of the array is not greater than M.

You should divide this array into K blocks of consecutive elements. The size of the block is any integer between 0 and N. Every element of the array should belong to some block.

The sum of the block from X to Y equals A[X] + A[X + 1] + ... + A[Y]. The sum of empty block equals 0.

The large sum is the maximal sum of any block.

For example, you are given integers K = 3, M = 5 and array A such that:

A = 2 A = 1 A = 5 A = 1 A = 2 A = 2 A = 2

The array can be divided, for example, into the following blocks:

• [2, 1, 5, 1, 2, 2, 2], [], [] with a large sum of 15;
• , [1, 5, 1, 2], [2, 2] with a large sum of 9;
• [2, 1, 5], [], [1, 2, 2, 2] with a large sum of 8;
• [2, 1], [5, 1], [2, 2, 2] with a large sum of 6.

The goal is to minimize the large sum. In the above example, 6 is the minimal large sum.

Write a function:

class Solution { public int solution(int K, int M, int[] A); }

that, given integers K, M and a non-empty array A consisting of N integers, returns the minimal large sum.

For example, given K = 3, M = 5 and array A such that:

A = 2 A = 1 A = 5 A = 1 A = 2 A = 2 A = 2

the function should return 6, as explained above.

Write an efficient algorithm for the following assumptions:

• N and K are integers within the range [1..100,000];
• M is an integer within the range [0..10,000];
• each element of array A is an integer within the range [0..M].