Given positive integers b and n, find an integer a such that an is as close as possible to b. (The result a is an approximation to the n-th root of b.)

Note that an may be less than, equal to, or greater than b.

Input

Consists of one or more pairs of values for b and n. Each pair appears on a single line, delimited by a single space. A line specifying the value zero for both b and n marks the end of the input. The value of b will be in the range 1 to 106 (inclusive), and the value of n will be in the range 1 to 9 (inclusive).

Output

For each pair b and n print a as defined above on a line by itself.