Enough Array

AtCoder

IDabc130_d

Time2000ms

Memory256MB

Difficulty—

You are given a sequence of positive integers of length $N$, $A=a_1,a_2,…,a_{N}$, and an integer $K$. How many contiguous subsequences of $A$ satisfy the following condition? * (Condition) The sum of the elements in the contiguous subsequence is at least $K$. We consider two contiguous subsequences different if they derive from different positions in $A$, even if they are the same in content. Note that the answer may not fit into a $32$\-bit integer type. ## Constraints * $1 \leq a_i \leq 10^5$ * $1 \leq N \leq 10^5$ * $1 \leq K \leq 10^{10}$ ## Input Input is given from Standard Input in the following format: $N$ $K$ $a_1$ $a_2$ $...$ $a_N$ [samples]

Samples

Input #1

4 10
6 1 2 7

Output #1

2

The following two contiguous subsequences satisfy the condition:

*   $A[1..4]=a_1,a_2,a_3,a_4$, with the sum of $16$
*   $A[2..4]=a_2,a_3,a_4$, with the sum of $10$

Input #2

3 5
3 3 3

Output #2

3

Note again that we consider two contiguous subsequences different if they derive from different positions, even if they are the same in content.

Input #3

10 53462
103 35322 232 342 21099 90000 18843 9010 35221 19352

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Enough Array",
    "description": {
      "content": "You are given a sequence of positive integers of length $N$, $A=a_1,a_2,…,a_{N}$, and an integer $K$. How many contiguous subsequences of $A$ satisfy the following condition? *   (Condition) The sum ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc130_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence of positive integers of length $N$, $A=a_1,a_2,…,a_{N}$, and an integer $K$. How many contiguous subsequences of $A$ satisfy the following condition?\n\n*   (Condition) The sum ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments