Buggy python submission (verdict: Time Limit Exceeded):
import collections
from functools import reduce
from operator import mul


def trial_division(n):
    l = []
    f = 2
    while n > 1:
        if n % f == 0:
            l.append(f)
            n /= f
        else:
            f += 1
    return l


def combinations_count(n, r):
    r = min(n - r, r)
    if r == 0:
        return 1
    return reduce(mul, range(n, n - r, -1)) // reduce(mul, range(r, 0, -1))


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

c = collections.Counter(trial_division(M))
a = 1
for i in c.values():
    a *= combinations_count(i + N - 1, i)

print(a % (10**9 + 7))


Fixed submission:
import collections
from functools import reduce
from operator import mul


def trial_division(n):
    l = []
    f = 2
    while f * f <= n:
        if n % f == 0:
            l.append(f)
            n //= f
        else:
            f += 1
    if n > 1:
        l.append(n)
    return l


def combinations_count(n, r):
    r = min(n - r, r)
    if r == 0:
        return 1
    return reduce(mul, range(n, n - r, -1)) // reduce(mul, range(r, 0, -1))


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

c = collections.Counter(trial_division(M))
a = 1
for i in c.values():
    a *= combinations_count(i + N - 1, i)

print(a % (10**9 + 7))

Buggy python submission (verdict: Time Limit Exceeded):
import collections
from functools import reduce
from operator import mul


def trial_division(n):
    l = []
    f = 2
    while n > 1:
        if n % f == 0:
            l.append(f)
            n /= f
        else:
            f += 1
    return l


def combinations_count(n, r):
    r = min(n - r, r)
    if r == 0:
        return 1
    return reduce(mul, range(n, n - r, -1)) // reduce(mul, range(r, 0, -1))


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

c = collections.Counter(trial_division(M))
a = 1
for i in c.values():
    a *= combinations_count(i + N - 1, i)

print(a % (10**9 + 7))


Fixed submission:
import collections
from functools import reduce
from operator import mul


def trial_division(n):
    l = []
    f = 2
    while f * f <= n:
        if n % f == 0:
            l.append(f)
            n //= f
        else:
            f += 1
    if n > 1:
        l.append(n)
    return l


def combinations_count(n, r):
    r = min(n - r, r)
    if r == 0:
        return 1
    return reduce(mul, range(n, n - r, -1)) // reduce(mul, range(r, 0, -1))


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

c = collections.Counter(trial_division(M))
a = 1
for i in c.values():
    a *= combinations_count(i + N - 1, i)

print(a % (10**9 + 7))

Buggy python submission (verdict: Time Limit Exceeded):
import collections
from functools import reduce
from operator import mul


def trial_division(n):
    l = []
    f = 2
    while n > 1:
        if (n % f == 0):
            l.append(f)
            n /= f
        else:
            f += 1
    return l


def combinations_count(n, r):
    r = min(n - r, r)
    if r == 0:
        return 1
    return reduce(mul, range(n, n - r, -1)) // reduce(mul, range(r, 0, -1))


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

c = collections.Counter(trial_division(M))
a = 1
for i in c.values():
    a *= combinations_count(i + N - 1, i)

print(a % (10**9 + 7))

Fixed submission:
import collections
from functools import reduce
from operator import mul


def trial_division(n):
    l = []
    f = 2
    while f * f <= n:
        if n % f == 0:
            l.append(f)
            n //= f
        else:
            f += 1
    if n > 1:
        l.append(n)
    return l


def combinations_count(n, r):
    r = min(n - r, r)
    if r == 0:
        return 1
    return reduce(mul, range(n, n - r, -1)) // reduce(mul, range(r, 0, -1))


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

c = collections.Counter(trial_division(M))
a = 1
for i in c.values():
    a *= combinations_count(i + N - 1, i)

print(a % (10**9 + 7))

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


def trial_division(n):
    l = []
    f = 2
    while n > 1:
        if (n % f == 0):
            l.append(f)
            n /= f
        else:
            f += 1
    return l


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


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

c = collections.Counter(trial_division(M))
a = 1
for i in c.values():
    a *= combinations_count(i + N - 1, i)

print(a % (10**9 + 7))

Fixed submission:
import collections
from functools import reduce
from operator import mul


def trial_division(n):
    l = []
    f = 2
    while f * f <= n:
        if n % f == 0:
            l.append(f)
            n //= f
        else:
            f += 1
    if n > 1:
        l.append(n)
    return l


def combinations_count(n, r):
    r = min(n - r, r)
    if r == 0:
        return 1
    return reduce(mul, range(n, n - r, -1)) // reduce(mul, range(r, 0, -1))


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

c = collections.Counter(trial_division(M))
a = 1
for i in c.values():
    a *= combinations_count(i + N - 1, i)

print(a % (10**9 + 7))