Pedometer

AtCoder

IDabc367_d

Time2000ms

Memory256MB

Difficulty—

There are $N$ rest areas around a lake. The rest areas are numbered $1$, $2$, ..., $N$ in clockwise order. It takes $A_i$ steps to walk clockwise from rest area $i$ to rest area $i+1$ (where rest area $N+1$ refers to rest area $1$). The minimum number of steps required to walk clockwise from rest area $s$ to rest area $t$ ($s \neq t$) is a multiple of $M$. Find the number of possible pairs $(s,t)$. ## Constraints * All input values are integers * $2 \le N \le 2 \times 10^5$ * $1 \le A_i \le 10^9$ * $1 \le M \le 10^6$ ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

4 3
2 1 4 3

Output #1

* The minimum number of steps to walk clockwise from rest area $1$ to rest area $2$ is $2$, which is not a multiple of $3$.
* The minimum number of steps to walk clockwise from rest area $1$ to rest area $3$ is $3$, which is a multiple of $3$.
* The minimum number of steps to walk clockwise from rest area $1$ to rest area $4$ is $7$, which is not a multiple of $3$.
* The minimum number of steps to walk clockwise from rest area $2$ to rest area $3$ is $1$, which is not a multiple of $3$.
* The minimum number of steps to walk clockwise from rest area $2$ to rest area $4$ is $5$, which is not a multiple of $3$.
* The minimum number of steps to walk clockwise from rest area $2$ to rest area $1$ is $8$, which is not a multiple of $3$.
* The minimum number of steps to walk clockwise from rest area $3$ to rest area $4$ is $4$, which is not a multiple of $3$.
* The minimum number of steps to walk clockwise from rest area $3$ to rest area $1$ is $7$, which is not a multiple of $3$.
* The minimum number of steps to walk clockwise from rest area $3$ to rest area $2$ is $9$, which is a multiple of $3$.
* The minimum number of steps to walk clockwise from rest area $4$ to rest area $1$ is $3$, which is a multiple of $3$.
* The minimum number of steps to walk clockwise from rest area $4$ to rest area $2$ is $5$, which is not a multiple of $3$.
* The minimum number of steps to walk clockwise from rest area $4$ to rest area $3$ is $6$, which is a multiple of $3$.

Therefore, there are four possible pairs $(s,t)$.

Input #2

2 1000000
1 1

Output #2

Input #3

9 5
9 9 8 2 4 4 3 5 3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Pedometer",
    "description": {
      "content": "There are $N$ rest areas around a lake.   The rest areas are numbered $1$, $2$, ..., $N$ in clockwise order.   It takes $A_i$ steps to walk clockwise from rest area $i$ to rest area $i+1$ (where rest ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc367_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ rest areas around a lake.  \nThe rest areas are numbered $1$, $2$, ..., $N$ in clockwise order.  \nIt takes $A_i$ steps to walk clockwise from rest area $i$ to rest area $i+1$ (where rest ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments