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Given positive integers $B$ and $N$, write a program that finds the positive integer $A$ whose $A^N$ is closest to $B$. In other words, output the $A$ that minimizes $|A^N - B|$. Note that $A^N$ may be less than, equal to, or greater than $B$.

The input consists of several test cases. Each test case is a single line containing two integers $B$ and $N$ separated by a space. ($1 \le B \le 1{,}000{,}000$, $1 \le N \le 9$)

The last line of the input contains two zeros; this line is not processed.

For each test case, output the corresponding $A$ on its own line.