Problem Statement

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

• $2 ≤ N ≤ 10^5$
• $0 ≤ a_i ≤ 10^9$
• $0 ≤ x ≤ 10^9$

Input

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

N x
a_1 a_2 ... a_N

Output

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