Candy Distribution

AtCoder

IDabc105_d

Time2000ms

Memory256MB

Difficulty—

There are $N$ boxes arranged in a row from left to right. The $i$\-th box from the left contains $A_i$ candies. You will take out the candies from some consecutive boxes and distribute them evenly to $M$ children. Such being the case, find the number of the pairs $(l, r)$ that satisfy the following: * $l$ and $r$ are both integers and satisfy $1 \leq l \leq r \leq N$. * $A_l + A_{l+1} + ... + A_r$ is a multiple of $M$. ## Constraints * All values in input are integers. * $1 \leq N \leq 10^5$ * $2 \leq M \leq 10^9$ * $1 \leq A_i \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

3 2
4 1 5

Output #1

3

The sum $A_l + A_{l+1} + ... + A_r$ for each pair $(l, r)$ is as follows:

*   Sum for $(1, 1)$: $4$
*   Sum for $(1, 2)$: $5$
*   Sum for $(1, 3)$: $10$
*   Sum for $(2, 2)$: $1$
*   Sum for $(2, 3)$: $6$
*   Sum for $(3, 3)$: $5$

Among these, three are multiples of $2$.

Input #2

13 17
29 7 5 7 9 51 7 13 8 55 42 9 81

Output #2

Input #3

10 400000000
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Candy Distribution",
    "description": {
      "content": "There are $N$ boxes arranged in a row from left to right. The $i$\\-th box from the left contains $A_i$ candies. You will take out the candies from some consecutive boxes and distribute them evenly to ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc105_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ boxes arranged in a row from left to right. The $i$\\-th box from the left contains $A_i$ candies.\nYou will take out the candies from some consecutive boxes and distribute them evenly to ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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