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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n,m=gets.chomp.split(" ").map(&:to_i)
ans=1
m_yaku=[]
i=2
sum=0
def kaijo(num)
  ans=1
  for i in 1..num do
    ans*=i
  end
  return ans
end
while i<=m do
  while m%i==0 do
    m/=i
    sum+=1
  end
  if sum!=0 then
    m_yaku.push([i,sum])
  end
  sum=0
  i+=1
end
for i in 0..m_yaku.length-1 do
  ans*=kaijo(n-1+m_yaku[i][1])/(kaijo(n-1)*kaijo(m_yaku[i][1]))
end
p ans%(10**9+7)