Meaningful Mean

AtCoder

IDarc075_c

Time2000ms

Memory256MB

Difficulty—

You are given an integer sequence of length $N$, $a =$ {$a_1, a_2, …, a_N$}, and an integer $K$. $a$ has $N(N+1)/2$ non-empty contiguous subsequences, {$a_l, a_{l+1}, …, a_r$} $(1 ≤ l ≤ r ≤ N)$. Among them, how many have an arithmetic mean that is greater than or equal to $K$? ## Constraints * All input values are integers. * $1 ≤ N ≤ 2 \times 10^5$ * $1 ≤ K ≤ 10^9$ * $1 ≤ a_i ≤ 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $K$ $a_1$ $a_2$ $:$ $a_N$ [samples]

Samples

Input #1

Output #1

5

All the non-empty contiguous subsequences of $a$ are listed below:

*   {$a_1$} = {$7$}
*   {$a_1, a_2$} = {$7, 5$}
*   {$a_1, a_2, a_3$} = {$7, 5, 7$}
*   {$a_2$} = {$5$}
*   {$a_2, a_3$} = {$5, 7$}
*   {$a_3$} = {$7$}

Their means are $7$, $6$, $19/3$, $5$, $6$ and $7$, respectively, and five among them are $6$ or greater. Note that {$a_1$} and {$a_3$} are indistinguishable by the values of their elements, but we count them individually.

Input #2

1 2
1

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Meaningful Mean",
    "description": {
      "content": "You are given an integer sequence of length $N$, $a =$ {$a_1, a_2, …, a_N$}, and an integer $K$. $a$ has $N(N+1)/2$ non-empty contiguous subsequences, {$a_l, a_{l+1}, …, a_r$} $(1 ≤ l ≤ r ≤ N)$. Among",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc075_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence of length $N$, $a =$ {$a_1, a_2, …, a_N$}, and an integer $K$.\n$a$ has $N(N+1)/2$ non-empty contiguous subsequences, {$a_l, a_{l+1}, …, a_r$} $(1 ≤ l ≤ r ≤ N)$. Among...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments