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



Sample input:
2 6


Sample output:
4

Submission status: Wrong Answer

Solution code:
MOD=10**9 + 7
N,M=map(int,input().split())
plist = 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dic = {}
for p in plist:
    dic[p] = 0
for p in plist:
    while M%p == 0:
        M/=p
        dic[p]+=1
L = N + 40
fact = [1 for _ in range(L)]
invfact = [1 for _ in range(L)]
for i in range(1,L):
    fact[i]=(fact[i-1]*i)%MOD
    invfact[i]=(invfact[i-1]*pow(i,MOD-2,MOD))%MOD
ans = 1
for p in dic:
    if dic[p] !=0:
        ans *= fact[N-1+dic[p]]*invfact[N-1]*invfact[dic[p]] %MOD
        ans = ans%MOD
print(ans)

Submission status: Wrong Answer

Solution code:
n,m=map(int,input().split())
pw = []
d = 2
while d*d <= m:
  e = 0
  while m % d == 0:
    e += 1
    m //= d
  if e > 0: pw.append(e)
  d += 1
ans = 1
for e in pw:
  comb = 1
  for i in range(e):
    comb = comb * (n+i) // (1+i)
  ans = ans * comb % 1000000007
print(ans)