Given two positive integers n and t. Find the smallest positive integer k such that there exist k positive integers a1, a2, …, ak that satisfy the following equation:

(a1 + t)*(a2 + t)*...*(ak + t) = n*a1*a2*...*ak

If there is no such k, output -1.
Constraints: 1 <= n, t <= 1000.
Examples:

>>> 4    1
            <<< 2
>>> 43   1
            <<< 7
>>> 47   1
            <<< 8
>>> 167  1
            <<< 10
>>> 172  1
            <<< 9
>>> 283  1
            <<< 11
>>> 299  1
            <<< 10
>>> 395  1
            <<< 11
>>> 571  1
            <<< 12
>>> 947  1
            <<< 14
>>> 997  1
            <<< 13
>>> 1    1
            <<< -1
>>> 5    2
            <<< 2

This is a number theory programming problem that i could not solve, and no one that i asked could solve it either, I think it is NP-hard.
I tried making a table answers[1001][1001] but don’t even know how to set it up as it will take a long time