Buggy python submission (verdict: Time Limit Exceeded):
from collections import Counter
import math
n,m = map(int, input().split())
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def prime_decomposition(n, table):
    i = 2
    while i * i <= n:
        while n % i == 0:
            n /= i
            table.append(i)
        i += 1
    if n > 1:
        table.append(n)
table = []
prime_decomposition(m, table)
c = Counter(table).values()
cc = Counter(c)
ans = 1
N = n-1
for i,j in cc.items():
  ans *= ((combinations_count(N+i,i))**j)%(10**9+7)
print(ans%(10**9+7))


Fixed submission:
from collections import Counter
import math
n,m = map(int, input().split())
def combinations_count(n, r):
    l = 1
    for num in range(1,r+1):
      l *= (n+num)
      l = l // num
    return l
def prime_decomposition(n, table):
    i = 2
    while i * i <= n:
        while n % i == 0:
            n /= i
            table.append(i)
        i += 1
    if n > 1:
        table.append(n)
table = []
prime_decomposition(m, table)
c = Counter(table).values()
cc = Counter(c)
ans = 1
N = n-1
for i,j in cc.items():
  ans *= ((combinations_count(N,i))**j)%(10**9+7)
print(ans%(10**9+7))

Buggy python submission (verdict: Time Limit Exceeded):
from collections import Counter
import math
n,m = map(int, input().split())
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def prime_decomposition(n, table):
    N = n**(1/2)
    i = 2
    while i <= N:
        while n % i == 0:
            n /= i
            table.append(i)
        i += 1
    if n > 1:
        table.append(n)
table = []
prime_decomposition(m, table)
c = Counter(table).values()
cc = Counter(c)
ans = 1
N = n-1
for i,j in cc.items():
  ans *= (combinations_count(N+i,i))**j
print(ans%(10**9+7))

Fixed submission:
from collections import Counter
import math
n,m = map(int, input().split())
def combinations_count(n, r):
    l = 1
    for num in range(1,r+1):
      l *= (n+num)
      l = l // num
    return l
def prime_decomposition(n, table):
    i = 2
    while i * i <= n:
        while n % i == 0:
            n /= i
            table.append(i)
        i += 1
    if n > 1:
        table.append(n)
table = []
prime_decomposition(m, table)
c = Counter(table).values()
cc = Counter(c)
ans = 1
N = n-1
for i,j in cc.items():
  ans *= ((combinations_count(N,i))**j)%(10**9+7)
print(ans%(10**9+7))

Buggy python submission (verdict: Time Limit Exceeded):
from collections import Counter
import math
n,m = map(int, input().split())
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def prime_decomposition(n, table):
    i = 2
    while i * i <= n:
        while n % i == 0:
            n /= i
            table.append(i)
        i += 1
    if n > 1:
        table.append(n)
table = []
prime_decomposition(m, table)
c = Counter(table).values()
cc = Counter(c)
ans = 1
N = n-1
for i,j in cc.items():
  ans *= (combinations_count(N+i,i))**j
print(ans%(10**9+7))

Fixed submission:
from collections import Counter
import math
n,m = map(int, input().split())
def combinations_count(n, r):
    l = 1
    for num in range(1,r+1):
      l *= (n+num)
      l = l // num
    return l
def prime_decomposition(n, table):
    i = 2
    while i * i <= n:
        while n % i == 0:
            n /= i
            table.append(i)
        i += 1
    if n > 1:
        table.append(n)
table = []
prime_decomposition(m, table)
c = Counter(table).values()
cc = Counter(c)
ans = 1
N = n-1
for i,j in cc.items():
  ans *= ((combinations_count(N,i))**j)%(10**9+7)
print(ans%(10**9+7))