{"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 possible greatest common divisor of $a_1, a_2, ..., a_N$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^{12}$\n*   $1 \\leq P \\leq 10^{12}$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $P$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"caddi2018_a","tags":[],"sample_group":[["3 24","2\n\nThe greatest common divisor would be $2$ when, for example, $a_1=2, a_2=6$ and $a_3=2$."],["5 1","1\n\nAs $a_i$ are positive integers, the only possible case is $a_1 = a_2 = a_3 = a_4 = a_5 = 1$."],["1 111","111"],["4 972439611840","206"]],"created_at":"2026-03-03 11:01:13"}}