SP18857 GOPI_SW - Gopi and Sandwich

Gopi is fond of sandwiches. Once his friend asks him to give part of his sandwich. But, Gopi wants to give him as little sandwich as possible. So, he devices a method. He divides the sandwich into **n** parts, where each part is a unit fraction( fractions of the form **1/p** where p is integer) of the original sandwich. Among all these parts he chooses the smallest part and gives it to his friend. Help Gopi to find the smallest part possible.

First line contains **t(1

Output one line per test case containing the denominator of the smallest part. Since, the answer can be very large, print **Answer modulo 10 $ ^{9} $ + 7**