Boxes and Candies

AtCoder

IDarc064_a

Time2000ms

Memory256MB

Difficulty—

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: $N$ $x$ $a_1$ $a_2$ $...$ $a_N$ [samples]

Samples

Input #1

3 3
2 2 2

Output #1

1

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

Input #2

6 1
1 6 1 2 0 4

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

Input #3

5 9
3 1 4 1 5

Output #3

0

The objective is already achieved without performing operations.

Input #4

2 0
5 5

Output #4

10

All the candies need to be eaten.

API Response (JSON)

{
  "problem": {
    "name": "Boxes and Candies",
    "description": {
      "content": "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 l",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc064_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ boxes arranged in a row. Initially, the $i$\\-th box from the left contains $a_i$ candies.\nSnuke can perform the following operation any number of times:\n\n*   Choose a box containing at l...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments