Problem 44782. Highest powers in factorials

This is the inverse of the problem Exponents in Factorials. Instead of being given a number and finding out the highest exponent it can be raised to for a given factorial, you'll be given a power, and you're being asked to find the highest number that can be raised to that power for a given factorial.

For example, n=7 and p=2. The highest perfect square (p=2) that can evenly divide 5040 (n=7, and 7!=5040) is 144, or 12^2. Therefore, your output should be y=12.

As before, you can assume that both n and power are integers greater than 1.