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

N, M = [int(x) for x in input().split()]
MOD = 10 ** 9 + 7

divisor = []
dict = {}

m = M
d = 2
while m != 1:
    while m % d == 0:
        # divisor.append(d)
        m //= d
        dict[d] = dict.get(d, 0) + 1
    d += 1
C = dict.values()
ret = 1


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

def combinations_count(n, r):
    a = max(r, n-r)
    b = min(r, n-r)
    r = 1
    for i in range(a+1, n+1):
        r *= i
    return r // math.factorial(b)


for c in C:
    ret *= combinations_count(c + N - 1, c)
    ret %= MOD

print(ret)


Fixed submission:
import math

N, M = [int(x) for x in input().split()]
MOD = 10 ** 9 + 7

divisor = []
dict = {}

m = M
d = 2
while m != 1:
    while m % d == 0:
        # divisor.append(d)
        m //= d
        dict[d] = dict.get(d, 0) + 1
    d += 1
C = dict.values()
ret = 1


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

def combinations_count(n, r):
    a = max(r, n-r)
    b = min(r, n-r)
    r = 1
    for i in range(a+1, n+1):
        r *= i
    return r // math.factorial(b)


for c in C:
    ret *= combinations_count(c + N - 1, c)
    ret %= MOD

print(ret)

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

N, M = [int(x) for x in input().split()]
MOD = 10 ** 9 + 7

divisor = []
dict = {}

m = M
d = 2
while m != 1:
    while m % d == 0:
        # divisor.append(d)
        m //= d
        dict[d] = dict.get(d, 0) + 1
    d += 1
C = dict.values()
ret = 1


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

def combinations_count(n, r):
    a = max(r, n-r)
    b = min(r, n-r)
    r = 1
    for i in range(a+1, n+1):
        r *= i
    return r // math.factorial(b)


for c in C:
    ret *= combinations_count(c + N - 1, c)
    ret %= MOD

print(ret)


Fixed submission:
import math

N, M = [int(x) for x in input().split()]
MOD = 10 ** 9 + 7

divisor = []
dict = {}

m = M
d = 2
while m != 1:
    while m % d == 0:
        # divisor.append(d)
        m //= d
        dict[d] = dict.get(d, 0) + 1
    d += 1
C = dict.values()
ret = 1


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

def combinations_count(n, r):
    a = max(r, n-r)
    b = min(r, n-r)
    r = 1
    for i in range(a+1, n+1):
        r *= i
    return r // math.factorial(b)


for c in C:
    ret *= combinations_count(c + N - 1, c)
    ret %= MOD

print(ret)

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

N, M = [int(x) for x in input().split()]
MOD = 10 ** 9 + 7

divisor = []
dict = {}

m = M
d = 2
while m != 1:
    while m % d == 0:
        # divisor.append(d)
        m //= d
        dict[d] = dict.get(d, 0) + 1
    d += 1
C = dict.values()
ret = 1


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


for c in C:
    ret *= combinations_count(c + N - 1, c)
    ret %= MOD

print(ret)


Fixed submission:
import math

N, M = [int(x) for x in input().split()]
MOD = 10 ** 9 + 7

divisor = []
dict = {}

m = M
d = 2
while m != 1:
    while m % d == 0:
        # divisor.append(d)
        m //= d
        dict[d] = dict.get(d, 0) + 1
    d += 1
C = dict.values()
ret = 1


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

def combinations_count(n, r):
    a = max(r, n-r)
    b = min(r, n-r)
    r = 1
    for i in range(a+1, n+1):
        r *= i
    return r // math.factorial(b)


for c in C:
    ret *= combinations_count(c + N - 1, c)
    ret %= MOD

print(ret)

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

N, M = [int(x) for x in input().split()]
MOD = 10**9 + 7

divisor = []
dict = {}

m = M
d = 2
while m != 1:
    while m % d == 0:
        divisor.append(d)
        m //= d
        dict[d] = dict.get(d,0) + 1
    d += 1
C = dict.values()
ret = 1

for c in C:
    ret = ret * math.factorial(c + N - 1)
    ret = ret // math.factorial(c)
    ret = ret // math.factorial(N - 1)
    ret = ret % MOD

print(ret)




Fixed submission:
import math

N, M = [int(x) for x in input().split()]
MOD = 10 ** 9 + 7

divisor = []
dict = {}

m = M
d = 2
while m != 1:
    while m % d == 0:
        # divisor.append(d)
        m //= d
        dict[d] = dict.get(d, 0) + 1
    d += 1
C = dict.values()
ret = 1


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

def combinations_count(n, r):
    a = max(r, n-r)
    b = min(r, n-r)
    r = 1
    for i in range(a+1, n+1):
        r *= i
    return r // math.factorial(b)


for c in C:
    ret *= combinations_count(c + N - 1, c)
    ret %= MOD

print(ret)