题目描述
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}.
输入格式
见题面
输出格式
见题面