Product and GCD

AtCoder

IDcaddi2018_a

Time2000ms

Memory256MB

Difficulty—

There are $N$ integers $a_1, a_2, ..., a_N$ not less than $1$. The values of $a_1, a_2, ..., a_N$ are not known, but it is known that $a_1 \times a_2 \times ... \times a_N = P$. Find the maximum possible greatest common divisor of $a_1, a_2, ..., a_N$. ## Constraints * $1 \leq N \leq 10^{12}$ * $1 \leq P \leq 10^{12}$ ## Input Input is given from Standard Input in the following format: $N$ $P$ [samples]

Samples

Input #1

3 24

Output #1

2

The greatest common divisor would be $2$ when, for example, $a_1=2, a_2=6$ and $a_3=2$.

Input #2

5 1

Output #2

1

As $a_i$ are positive integers, the only possible case is $a_1 = a_2 = a_3 = a_4 = a_5 = 1$.

Input #3

1 111

Output #3

Input #4

4 972439611840

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Product and GCD",
    "description": {
      "content": "There are $N$ integers $a_1, a_2, ..., a_N$ not less than $1$. The values of $a_1, a_2, ..., a_N$ are not known, but it is known that $a_1 \\times a_2 \\times ... \\times a_N = P$. Find the maximum possi",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "caddi2018_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ integers $a_1, a_2, ..., a_N$ not less than $1$. The values of $a_1, a_2, ..., a_N$ are not known, but it is known that $a_1 \\times a_2 \\times ... \\times a_N = P$.\nFind the maximum possi...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments