## Problem 500!!!

### Problem 500

The number of divisors of 120 is 16.

In fact 120 is the smallest number having 16 divisors.

Find the smallest number with 2^{500500} divisors.

Give your answer modulo 500500507.

The number of divisors of 120 is 16.

In fact 120 is the smallest number having 16 divisors.

Find the smallest number with 2^{500500} divisors.

Give your answer modulo 500500507.