Score : 400 points
You are given positive integers N and M.
How many sequences a of length N consisting of positive integers satisfy a_1 \times a_2 \times ... \times a_N = M? Find the count modulo 10^9+7.
Here, two sequences a' and a'' are considered different when there exists some i such that a_i' \neq a_i''.
Input is given from Standard Input in the following format:
N M
Print the number of the sequences consisting of positive integers that satisfy the condition, modulo 10^9 + 7.
2 6
4
Four sequences satisfy the condition: \{a_1, a_2\} = \{1, 6\}, \{2, 3\}, \{3, 2\} and \{6, 1\}.
3 12
18
100000 1000000000
957870001