1000 - Minimum Cost to Merge Stones\.

Hard

There are n piles of stones arranged in a row. The <code>i^th</code> pile has stones[i] stones.

A move consists of merging exactly k consecutive piles into one pile, and the cost of this move is equal to the total number of stones in these k piles.

Return the minimum cost to merge all piles of stones into one pile. If it is impossible, return -1.

Example 1:

Input: stones = 3,2,4,1, k = 2

Output: 20

Explanation:

We start with 3, 2, 4, 1.

We merge 3, 2 for a cost of 5, and we are left with 5, 4, 1.

We merge 4, 1 for a cost of 5, and we are left with 5, 5.

We merge 5, 5 for a cost of 10, and we are left with 10.

The total cost was 20, and this is the minimum possible.

Example 2:

Input: stones = 3,2,4,1, k = 3

Output: -1

Explanation: After any merge operation, there are 2 piles left, and we can't merge anymore. So the task is impossible.

Example 3:

Input: stones = 3,5,1,2,6, k = 3

Output: 25

Explanation:

We start with 3, 5, 1, 2, 6.

We merge 5, 1, 2 for a cost of 8, and we are left with 3, 8, 6.

We merge 3, 8, 6 for a cost of 17, and we are left with 17.

The total cost was 25, and this is the minimum possible.

Constraints:

• n == stones.length

• 1 <= n <= 30

• 1 <= stones[i] <= 100

• 2 <= k <= 30