div2 srm 704 hard ModEquationEasy

Problem Statement

You are given the s n, K, and v.

Consider the following modular equation with n variables: (x[0] * x[1] * x[2] * ... * x[n-1]) mod K = v. How many solutions does it have?

Formally, we want to find the number of sequences (x[0], x[1], ..., x[n-1]) such that each x[i] is an integer between 0 and K-1, inclusive, and the product of all x[i] gives the remainder v when divided by K.

Please compute and return the number of such sequences, modulo 10⁹+7.

note

I used dynamic programing.

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