Buggy python submission (verdict: Time Limit Exceeded):
import math

N,M = list(map(int, input().split()))

X = {}
for i in range(2, M):
  if M == 1:
    break
  while True:
    if M % i == 0:
      if i in X:
        X[i] = X[i] + 1
      else:
        X[i] = 1
      M //= i
    else:
      break

def cmb(n, r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n;

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p;
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    return result;
       
sum = 1
for i in X.values():
  sum = (sum * cmb(i + N - 1, i) % 1000000007) % 1000000007
  
  
print(sum)

Fixed submission:
import math
import copy

####################
def prime_decomposition(n):
  i = 2
  X = {}
  while i * i <= n:
    while n % i == 0:
      n /= i
      if i in X:
        X[i] = X[i] + 1
      else:
        X[i] = 1
    i += 1
  if n > 1:
    X[n] = 1
  return X

def cmb(n, r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n;

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p;
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    return result;

####################
  
N,M = list(map(int, input().split()))

X = prime_decomposition(M)
       
sum = 1
for i in X.values():
  sum = (sum * cmb(i + N - 1, i) % 1000000007) % 1000000007
  
print(sum)

Buggy python submission (verdict: Time Limit Exceeded):
import math
N,M = list(map(int, input().split()))

X = {}
for i in range(2, M):
  if M == 1:
    break
  while True:
    if M % i == 0:
      if i in X:
        X[i] = X[i] + 1
      else:
        X[i] = 1
      M //= i
    else:
      break

def P(n,r):
  return math.factorial(n) // math.factorial(n-r)
def C(n,r):
  return P(n,r) // math.factorial(r)
       
sum = 1
for i in X.values():
  sum = (sum * C(i + N - 1, i) % 1000000007) % 1000000007
  
  
print(sum)

Fixed submission:
import math
import copy

####################
def prime_decomposition(n):
  i = 2
  X = {}
  while i * i <= n:
    while n % i == 0:
      n /= i
      if i in X:
        X[i] = X[i] + 1
      else:
        X[i] = 1
    i += 1
  if n > 1:
    X[n] = 1
  return X

def cmb(n, r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n;

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p;
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    return result;

####################
  
N,M = list(map(int, input().split()))

X = prime_decomposition(M)
       
sum = 1
for i in X.values():
  sum = (sum * cmb(i + N - 1, i) % 1000000007) % 1000000007
  
print(sum)