Product of Divisors

AtCoder

IDarc167_b

Time2000ms

Memory256MB

Difficulty—

At most how many times can the product of all positive divisors of $A^{B}$ be divided by $A$? It can be shown from the constraints that this count is finite, so find it modulo $998244353$. ## Constraints * $2\leq A\leq 10^{12}$ * $0\leq B\leq 10^{18}$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $A$ $B$ [samples]

Samples

Input #1

2 3

Output #1

6

The positive divisors of $A^{B}=8$ are $1$, $2$, $4$, and $8$, whose product is $64$. $64$ can be divided by $2$ at most six times, so print $6$.

Input #2

924 167

Output #2

867046524

Input #3

167167167167 0

Output #3

API Response (JSON)

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  "problem": {
    "name": "Product of Divisors",
    "description": {
      "content": "At most how many times can the product of all positive divisors of $A^{B}$ be divided by $A$? It can be shown from the constraints that this count is finite, so find it modulo $998244353$.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc167_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "At most how many times can the product of all positive divisors of $A^{B}$ be divided by $A$?\nIt can be shown from the constraints that this count is finite, so find it modulo $998244353$.\n\n## Constra...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments