问题 AP: Cut the Sequence

Given an integer sequencean an of length N, you are to cut the sequence into several parts every one of which is a consecutive subsequence of the original sequence. Every part must satisfy that the sum of the integers in the part is not greater than a given integer M. You are to find a cutting that minimizes the sum of the maximum integer of each part.

The first line of input contains two integer N (0<N≤100000), M. The following line contains N integers describes the integer sequence. Every integer in the sequence is between 0 and 1 000 000 inclusively.

Output one integer which is the minimum sum of the maximum integer of each part. If no such cuttings exist, output −1.

8 17
2 2 2 8 1 8 2 1

12