I'm trying to solve the following problem (from VOI 2005).

Given a sequence a with n numbers, find the minimum M such that there's a way to split sequence a into k non-empty continuous subsequence and the total sum of each subsequence does not exceed M.

Constrains: 1 <= k <= n <= 15000, |ai| <= 30000, ai may be negative.

The best solution I can come up for this problem is the following O(n^2*k) DP solution:

Call f[i][k] the minimum value M for the sequence that contain first i numbers, d[i] the sum of the first i number of sequence. Then we have the following formula: f[i][k] = min(max(f[j][k], d[i]-d[j])) (with 0 <= j < i)

Of course, with such big constrains, this solution is not fast enough. Is there a faster solution for this? Thanks in advance.