{"raw_statement":[{"iden":"problem statement","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 $a_1, a_2, ..., a_N$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^{12}$\n*   $1 \\leq P \\leq 10^{12}$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $P$"},{"iden":"sample input 1","content":"3 24"},{"iden":"sample output 1","content":"2\n\nThe greatest common divisor would be $2$ when, for example, $a_1=2, a_2=6$ and $a_3=2$."},{"iden":"sample input 2","content":"5 1"},{"iden":"sample output 2","content":"1\n\nAs $a_i$ are positive integers, the only possible case is $a_1 = a_2 = a_3 = a_4 = a_5 = 1$."},{"iden":"sample input 3","content":"1 111"},{"iden":"sample output 3","content":"111"},{"iden":"sample input 4","content":"4 972439611840"},{"iden":"sample output 4","content":"206"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}