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''.

-----Constraints-----

• All values in input are integers.
• 1 \leq N \leq 10^5
• 1 \leq M \leq 10^9

-----Input----- Input is given from Standard Input in the following format: N M

-----Output----- Print the number of the sequences consisting of positive integers that satisfy the condition, modulo 10^9 + 7.

-----Sample Input----- 2 6

-----Sample Output----- 4

Four sequences satisfy the condition: {a_1, a_2} = {1, 6}, {2, 3}, {3, 2} and {6, 1}.