100482: [AtCoder]ABC048 C - Boxes and Candies

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.

Sample Input 1

3 3
2 2 2

Sample Output 1

1

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

Sample Input 2

6 1
1 6 1 2 0 4

Sample Output 2

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 $(1, 0, 1, 0, 0, 1)$.

Sample Input 3

5 9
3 1 4 1 5

Sample Output 3

0

The objective is already achieved without performing operations.

Sample Input 4

2 0
5 5

Sample Output 4

10

All the candies need to be eaten.