Sentou

AtCoder

IDarc073_a

Time2000ms

Memory256MB

Difficulty—

In a public bath, there is a shower which emits water for $T$ seconds when the switch is pushed. If the switch is pushed when the shower is already emitting water, from that moment it will be emitting water for $T$ seconds. Note that it does not mean that the shower emits water for $T$ additional seconds. $N$ people will push the switch while passing by the shower. The $i$\-th person will push the switch $t_i$ seconds after the first person pushes it. How long will the shower emit water in total? ## Constraints * $1 ≤ N ≤ 200,000$ * $1 ≤ T ≤ 10^9$ * $0 = t_1 < t_2 < t_3 < , ..., < t_{N-1} < t_N ≤ 10^9$ * $T$ and each $t_i$ are integers. ## Input Input is given from Standard Input in the following format: $N$ $T$ $t_1$ $t_2$ ... $t_N$ [samples]

Samples

Input #1

2 4
0 3

Output #1

7

Three seconds after the first person pushes the water, the switch is pushed again and the shower emits water for four more seconds, for a total of seven seconds.

Input #2

2 4
0 5

Output #2

8

One second after the shower stops emission of water triggered by the first person, the switch is pushed again.

Input #3

4 1000000000
0 1000 1000000 1000000000

Output #3

2000000000

Input #4

1 1
0

Output #4

Input #5

9 10
0 3 5 7 100 110 200 300 311

Output #5

API Response (JSON)

{
  "problem": {
    "name": "Sentou",
    "description": {
      "content": "In a public bath, there is a shower which emits water for $T$ seconds when the switch is pushed. If the switch is pushed when the shower is already emitting water, from that moment it will be emitting",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc073_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In a public bath, there is a shower which emits water for $T$ seconds when the switch is pushed.\nIf the switch is pushed when the shower is already emitting water, from that moment it will be emitting...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments