Score : $300$ points

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

• $2 \leq N \leq 10^5$
• $0 \leq a_i \leq 10^9$
• $0 \leq x \leq 10^9$

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.

3 3
2 2 2

1

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

6 1
1 6 1 2 0 4

11

For example, eat six candies in the second box, two in the fourth box, and three in the sixth box. Then, the number of candies in each box becomes $(1, 0, 1, 0, 0, 1)$.

5 9
3 1 4 1 5

0

The objective is already achieved without performing operations.

2 0
5 5

10

All the candies need to be eaten.