Problem:
Score : 400 points

Problem Statement

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 1

2 6

Sample Output 1

4

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

Sample Input 2

3 12

Sample Output 2

18

Sample Input 3

100000 1000000000

Sample Output 3

957870001

Solution in PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

#! /usr/bin/env python
# -*- coding: utf-8 -*-
# vim:fenc=utf-8
#

"""
RC110 D
"""


n,m = map(int,input().split())

from math import sqrt
from collections import deque
def divisors(x):
    divs = deque()
    sx = int(sqrt(x))
    if x == sx**2:
        divs.append(sx)
        sx = sx-1
    for i in range(sx,0,-1):
        if x%i==0:
            divs.append(i)
            divs.appendleft(x//i)
    return(divs)

mdivs = list(divisors(m))
from collections import defaultdict
divsdict = defaultdict(list)
for d in mdivs:
    divsdict[d] = [dd for dd in mdivs if d%dd==0]

dpdict = defaultdict(int)
for d in mdivs:
    dpdict[d]=0
dpdict[1] = 1

cut = 10**9+7

for i in range(n):
    dpdicttmp = dpdict
    for d in mdivs:
        dpdict[d] = sum(map(lambda x:dpdict[x],divsdict[d]))%(10**9+7)

print(dpdict[m])