Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**6)

divisors = {}
def findDivisors(M):
    if M in divisors:
        return divisors[M]
    else:
        divisors[M] = [i for i in range(1, M + 1) if M % i == 0]
        return divisors[M]

def f(N, M):
    if N == 2:
        return len(findDivisors(int(M)))
    else:
        return sum([f(N-1, M / i) for i in findDivisors(int(M))])

def main():
    N, M = map(int, input().split())
    print(f(N, M) % (10 ** 9 + 7))

if __name__ == '__main__':
    main()

Fixed submission:
import math
import functools


def mmul(a, b, mod):
    return (a % mod) * (b % mod) % mod


def mfact(a, mod):
    fact = 1
    for m in range(a + 1):
        fact *= m % mod
        fact %= mod
    return fact


def mpow(a, b, mod):
    if b == 0:
        return 1
    if b == 1:
        return a % mod
    if b % 2 == 0:
        return mpow(a, b / 2, mod) ** 2 % mod
    return mpow(a, b // 2, mod) ** 2 * a % mod


def mdiv(a, b, mod):
    return mmul(a, mpow(b, mod - 2, mod), mod)


# (n+a)Ca = (n+a)! / n!a! mod mod for n >> a
def mnpaca(n, a, mod):
    res = 1
    for num in range(n + 1, n + a + 1):
        res *= num % mod
        res %= mod
    return mdiv(res, math.factorial(a), mod)


mod = 10 ** 9 + 7

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

prime_counts = []
i = 2
while i * i <= M:
    count = 0
    while M % i == 0:
        M /= i
        count += 1
    if count:
        prime_counts.append(count)
    i += 1
if M > 1:
    prime_counts.append(1)

res = functools.reduce(lambda x, y: x * y, [mnpaca(N - 1, c, mod) for c in prime_counts], 1)

print(res % mod)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**6)

divisors = {}
def findDivisors(M):
    if M in divisors:
        return divisors[M]
    else:
        divisors[M] = [i for i in range(1, M + 1) if M % i == 0]
        return divisors[M]

def f(N, M):
    if N == 2:
        return len(findDivisors(int(M)))
    else:
        return sum([f(N-1, M / i) for i in findDivisors(int(M))])

def main():
    N, M = map(int, input().split())
    print(f(N, M) % (10 ** 9 + 7))

if __name__ == '__main__':
    main()

Fixed submission:
import math
import functools


def mmul(a, b, mod):
    return (a % mod) * (b % mod) % mod


def mfact(a, mod):
    fact = 1
    for m in range(a + 1):
        fact *= m % mod
        fact %= mod
    return fact


def mpow(a, b, mod):
    if b == 0:
        return 1
    if b == 1:
        return a % mod
    if b % 2 == 0:
        return mpow(a, b / 2, mod) ** 2 % mod
    return mpow(a, b // 2, mod) ** 2 * a % mod


def mdiv(a, b, mod):
    return mmul(a, mpow(b, mod - 2, mod), mod)


# (n+a)Ca = (n+a)! / n!a! mod mod for n >> a
def mnpaca(n, a, mod):
    res = 1
    for num in range(n + 1, n + a + 1):
        res *= num % mod
        res %= mod
    return mdiv(res, math.factorial(a), mod)


mod = 10 ** 9 + 7

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

prime_counts = []
i = 2
while i * i <= M:
    count = 0
    while M % i == 0:
        M /= i
        count += 1
    if count:
        prime_counts.append(count)
    i += 1
if M > 1:
    prime_counts.append(1)

res = functools.reduce(lambda x, y: x * y, [mnpaca(N - 1, c, mod) for c in prime_counts], 1)

print(res % mod)