### Title

### 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.