#### Registered Users Only

Please login to utilize this feature.

Do note that this website only supports submissions in C++.

### 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:

Nxa_{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.

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 100 | 20 | 1s | 256MB | Minimum |

2 | 0 | 4 | 1s | 256MB | Minimum |

### Judge Compile Command

g++-8 ans.cpp -o candies2 -Wall -Wshadow -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512