SP7623 DIVISER9 - Divisors VI

Find the the smallest integer with exactly **N** odd divisors, where each divisor is greater or equal to 1 !!! For example for 3 odd divisors, 9 (factors 1, 3, 9) is minimum.

Each line contain **N (0 < N < 10 $ ^{14} $ )**. There are 100 inputs total.

One answer on each line for each **N**, **Modulo 1000000007.**