Candy Box

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Problem

There are N boxes arranged in a row. Initially, the i-th box from the left contains ai candies.

Snuke can perform the following operation any number of times:

Choose a box containing at least one candy, and eat one of the candies in the chosen box.

His objective is as follows:

Any two neighboring boxes contain at most x candies in total.

Find the minimum number of operations required to achieve the objective.

Constraints

2≤N≤105

0≤ai≤109

0≤x≤109

Input

The input is given from Standard Input in the following format:

N X
a1 a2 ..... aN

 

Output

Print the minimum number of operations required to achieve the objective.

Time Limit: 1
Memory Limit: 256
Source Limit:
Explanation

Eat one candy in the second box. Then, the number of candies in each box becomes (2,1,2)

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