Counting of Subarrays

AtCoder

IDagc037_f

Time2000ms

Memory256MB

Difficulty—

For a sequence $S$ of positive integers and positive integers $k$ and $l$, $S$ is said to belong to _level_ $(k,l)$ when one of the following conditions is satisfied: * The length of $S$ is $1$, and its only element is $k$. * There exist sequences $T_1,T_2,...,T_m$ ($m \geq l$) belonging to level $(k-1,l)$ such that the concatenation of $T_1,T_2,...,T_m$ in this order coincides with $S$. Note that the second condition has no effect when $k=1$, that is, a sequence belongs to level $(1,l)$ only if the first condition is satisfied. Given are a sequence of positive integers $A_1,A_2,...,A_N$ and a positive integer $L$. Find the number of subsequences $A_i,A_{i+1},...,A_j$ ($1 \leq i \leq j \leq N$) that satisfy the following condition: * There exists a positive integer $K$ such that the sequence $A_i,A_{i+1},...,A_j$ belongs to level $(K,L)$. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $2 \leq L \leq N$ * $1 \leq A_i \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $L$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

9 3
2 1 1 1 1 1 1 2 3

Output #1

22

For example, both of the sequences $(1,1,1)$ and $(2)$ belong to level $(2,3)$, so the sequence $(2,1,1,1,1,1,1)$ belong to level $(3,3)$.

Input #2

9 2
2 1 1 1 1 1 1 2 3

Output #2

Input #3

15 3
4 3 2 1 1 1 2 3 2 2 1 1 1 2 2

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Counting of Subarrays",
    "description": {
      "content": "For a sequence $S$ of positive integers and positive integers $k$ and $l$, $S$ is said to belong to _level_ $(k,l)$ when one of the following conditions is satisfied: *   The length of $S$ is $1$, an",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc037_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For a sequence $S$ of positive integers and positive integers $k$ and $l$, $S$ is said to belong to _level_ $(k,l)$ when one of the following conditions is satisfied:\n\n*   The length of $S$ is $1$, an...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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