Rem of Sum is Num

AtCoder

IDabc146_e

Time2000ms

Memory256MB

Difficulty—

Given are a sequence of $N$ positive integers $A_1, A_2, \ldots, A_N$, and a positive integer $K$. Find the number of non-empty contiguous subsequences in $A$ such that the remainder when dividing the sum of its elements by $K$ is equal to the number of its elements. We consider two subsequences different if they are taken from different positions, even if they are equal sequences. ## Constraints * All values in input are integers. * $1 \leq N \leq 2\times 10^5$ * $1 \leq K \leq 10^9$ * $1 \leq A_i \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

5 4
1 4 2 3 5

Output #1

4

Four sequences satisfy the condition: $(1)$, $(4,2)$, $(1,4,2)$, and $(5)$.

Input #2

8 4
4 2 4 2 4 2 4 2

Output #2

7

$(4,2)$ is counted four times, and $(2,4)$ is counted three times.

Input #3

10 7
14 15 92 65 35 89 79 32 38 46

Output #3

API Response (JSON)

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    "name": "Rem of Sum is Num",
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    "platform": "AtCoder",
    "limit": {
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      "memory_limit": 262144
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    "difficulty": "None",
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      "statement_type": "Markdown",
      "content": "Given are a sequence of $N$ positive integers $A_1, A_2, \\ldots, A_N$, and a positive integer $K$.\nFind the number of non-empty contiguous subsequences in $A$ such that the remainder when dividing the...",
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