Buggy python submission (verdict: Time Limit Exceeded):
import math
mod = 1000000007
N,M = list(map(int,input().strip().split()))
m_sqrt = int(math.sqrt(M))
def P(n, r):
  return math.factorial(n)//math.factorial(n-r)
def C(n, r):
  return P(n, r)//math.factorial(r)

ans = 1
cnt = 0
while  M%2 == 0:
  M = M//2
  cnt += 1
ans *= C(N+cnt-1,cnt)
cnt = 0

for i in range(3,m_sqrt+1,2):
  while M%i == 0:
    M = M//i
    cnt += 1
  if cnt != 0:
    ans *= C(N+cnt-1,cnt)
    cnt = 0
if M != 1:
    ans *= C(N,1)

print(ans%mod)


Fixed submission:
import math
mod = 1000000007
N,M = list(map(int,input().strip().split()))
l = []

def P(n, r):
  return math.factorial(n)//math.factorial(n-r)

def C(n, r):
  return P(n, r)//math.factorial(r)

ans = 1
cnt = 0
while  M%2 == 0:
  M //= 2
  cnt += 1
l.append(cnt)
cnt = 0

i = 3
while i**2 <= M:
  cnt = 0
  while M%i == 0:
    M //= i
    cnt += 1
  if cnt != 0:
    l.append(cnt)
    cnt = 0
  i += 2
if M != 1:
    l.append(1)

for i in l:
  for j in range(i):
    ans = ans*(N+j)//(j+1)

print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
import math
import collections
mod = 1000000007
N,M = list(map(int,input().strip().split()))

def prime_decomposition(n):
  i = 2
  table = []
  while i * i <= n:
    while n % i == 0:
      n /= i
      table.append(i)
    i += 1
  if n > 1:
    table.append(n)
  return table

def P(n, r):
  return math.factorial(n)//math.factorial(n-r)

def C(n, r):
  return P(n, r)//math.factorial(r)


l = list(collections.Counter(prime_decomposition(M)).values())


ans = 1
for i in l:
  ans *= C(N+i-1,i)
  
print(ans%mod)


Fixed submission:
import math
mod = 1000000007
N,M = list(map(int,input().strip().split()))
l = []

def P(n, r):
  return math.factorial(n)//math.factorial(n-r)

def C(n, r):
  return P(n, r)//math.factorial(r)

ans = 1
cnt = 0
while  M%2 == 0:
  M //= 2
  cnt += 1
l.append(cnt)
cnt = 0

i = 3
while i**2 <= M:
  cnt = 0
  while M%i == 0:
    M //= i
    cnt += 1
  if cnt != 0:
    l.append(cnt)
    cnt = 0
  i += 2
if M != 1:
    l.append(1)

for i in l:
  for j in range(i):
    ans = ans*(N+j)//(j+1)

print(ans%mod)

Buggy python submission (verdict: Time Limit Exceeded):
import math
mod = 1000000007
N,M = list(map(int,input().strip().split()))
l = []

def P(n, r):
  return math.factorial(n)//math.factorial(n-r)
def C(n, r):
  return P(n, r)//math.factorial(r)

cnt = 0
while  M%2 == 0:
  M = M//2
  cnt += 1
l.append(cnt)
  
i = 3
while M != 1:
  cnt = 0
  while M%i == 0:
    M = M//i
    cnt += 1
  if cnt != 0:
    l.append(cnt)
  i += 2
  
ans = 1
for i in l:
  ans *= C(N+i-1,i)
  
print(ans%mod)

Fixed submission:
import math
mod = 1000000007
N,M = list(map(int,input().strip().split()))
l = []

def P(n, r):
  return math.factorial(n)//math.factorial(n-r)

def C(n, r):
  return P(n, r)//math.factorial(r)

ans = 1
cnt = 0
while  M%2 == 0:
  M //= 2
  cnt += 1
l.append(cnt)
cnt = 0

i = 3
while i**2 <= M:
  cnt = 0
  while M%i == 0:
    M //= i
    cnt += 1
  if cnt != 0:
    l.append(cnt)
    cnt = 0
  i += 2
if M != 1:
    l.append(1)

for i in l:
  for j in range(i):
    ans = ans*(N+j)//(j+1)

print(ans%mod)

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

i = 2
cnt = 0
ans = 1
while True:
  if M%i == 0:
    M = M//i
    cnt += 1
  else:
    ans *= math.factorial(N+cnt-1) // (math.factorial(N-1)*math.factorial(cnt))
    i += 1
    cnt = 0
    if M == 1:
      break
      
print(ans%(10**9+7))

Fixed submission:
import math
mod = 1000000007
N,M = list(map(int,input().strip().split()))
l = []

def P(n, r):
  return math.factorial(n)//math.factorial(n-r)

def C(n, r):
  return P(n, r)//math.factorial(r)

ans = 1
cnt = 0
while  M%2 == 0:
  M //= 2
  cnt += 1
l.append(cnt)
cnt = 0

i = 3
while i**2 <= M:
  cnt = 0
  while M%i == 0:
    M //= i
    cnt += 1
  if cnt != 0:
    l.append(cnt)
    cnt = 0
  i += 2
if M != 1:
    l.append(1)

for i in l:
  for j in range(i):
    ans = ans*(N+j)//(j+1)

print(ans%mod)