Factorization

AtCoder

IDabc110_d

Time2000ms

Memory256MB

Difficulty—

You are given positive integers $N$ and $M$. How many sequences $a$ of length $N$ consisting of positive integers satisfy $a_1 \times a_2 \times ... \times a_N = M$? Find the count modulo $10^9+7$. Here, two sequences $a'$ and $a''$ are considered different when there exists some $i$ such that $a_i' \neq a_i''$. ## Constraints * All values in input are integers. * $1 \leq N \leq 10^5$ * $1 \leq M \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $M$ [samples]

Samples

Input #1

2 6

Output #1

4

Four sequences satisfy the condition: ${a_1, a_2} = {1, 6}, {2, 3}, {3, 2}$ and ${6, 1}$.

Input #2

3 12

Output #2

Input #3

100000 1000000000

Output #3

957870001

API Response (JSON)

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  "problem": {
    "name": "Factorization",
    "description": {
      "content": "You are given positive integers $N$ and $M$. How many sequences $a$ of length $N$ consisting of positive integers satisfy $a_1 \\times a_2 \\times ... \\times a_N = M$? Find the count modulo $10^9+7$. He",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc110_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given positive integers $N$ and $M$.\nHow many sequences $a$ of length $N$ consisting of positive integers satisfy $a_1 \\times a_2 \\times ... \\times a_N = M$? Find the count modulo $10^9+7$.\nHe...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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