Buggy python submission (verdict: Time Limit Exceeded):
import math
import os
import sys
from collections import Counter

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(2147483647)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7

N, M = list(map(int, sys.stdin.readline().split()))


def get_factors(n):
    """
    素因数分解
    :param int n:
    :rtype: list of int
    """
    if n <= 1:
        return []

    ret = []
    while n > 2 and n % 2 == 0:
        ret.append(2)
        n //= 2
    i = 3
    while i <= math.sqrt(n):
        if n % i == 0:
            ret.append(i)
            n //= i
        else:
            i += 2
    ret.append(n)
    return ret


def ncr(n, r, mod=None):
    """
    scipy.misc.comb または scipy.special.comb と同じ
    組み合わせの数 nCr
    :param int n:
    :param int r:
    :param int mod: 3 以上の素数であること
    :rtype: int
    """
    if n < r:
        return 0

    return math.factorial(n) // math.factorial(r) // math.factorial(n - r)


factors = get_factors(M)

ans = 1
for c in Counter(factors).values():
    # N 個の箱から重複ありで c 個選ぶ
    ans = ans * ncr(N + c - 1, c) % MOD
print(ans)


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


def get_factors(n):
    """
    素因数分解
    :param int n:
    :type: list of int
    """
    if n <= 1:
        return []

    ret = []
    while n > 2 and n % 2 == 0:
        ret.append(2)
        n //= 2
    i = 3
    while i <= math.sqrt(n):
        if n % i == 0:
            ret.append(i)
            n //= i
        else:
            i += 2
    ret.append(n)
    return ret


def comb(n, r):
    """
    組み合わせの数 nCr
    :param n:
    :param r:
    :return:
    """
    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())
MOD = 10 ** 9 + 7

# divs = sorted(get_divisors(m))
# # dp[d]: 累積積が d となる数列の数
# dp = {d: 1 for d in divs}
# for _ in range(n - 1):
#     for i in reversed(range(len(divs))):
#         div = divs[i]
#         dp[div] = sum([dp[d] for d in divs if div % d == 0]) % MOD
#     print(dp)
# print(dp)
# おそい


factors = get_factors(m)
counts = Counter(factors)
# k**v を全部かけあわせたやつが m に一致する
# print(functools.reduce(operator.mul, [k ** v for k, v in counts.items()]))

# v 個の k を n 個の数に配分する組み合わせの数
# → v + (n-1) 個のスペースへの v の置き方の組み合わせの数
ans = 1
for k, v in counts.items():
    ans *= comb(v + (n - 1), v)
    ans %= MOD
print(ans)

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


def get_factors(n):
    """
    素因数分解
    :param int n:
    :type: list of int
    """
    if n <= 1:
        return []

    ret = []
    while n > 2 and n % 2 == 0:
        ret.append(2)
        n //= 2
    i = 3
    while i <= n / 2:
        if n % i == 0:
            ret.append(i)
            n //= i
        else:
            i += 2
    ret.append(n)
    return ret


def comb(n, r):
    """
    組み合わせの数 nCr
    :param n:
    :param r:
    :return:
    """
    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())
MOD = 10 ** 9 + 7

# divs = sorted(get_divisors(m))
# # dp[d]: 累積積が d となる数列の数
# dp = {d: 1 for d in divs}
# for _ in range(n - 1):
#     for i in reversed(range(len(divs))):
#         div = divs[i]
#         dp[div] = sum([dp[d] for d in divs if div % d == 0]) % MOD
#     print(dp)
# print(dp)
# おそい


factors = get_factors(m)
counts = Counter(factors)
# k**v を全部かけあわせたやつが m に一致する
# print(functools.reduce(operator.mul, [k ** v for k, v in counts.items()]))

# v 個の k を n 個の数に配分する組み合わせの数
# → v + (n-1) 個のスペースへの v の置き方の組み合わせの数
ans = 1
for k, v in counts.items():
    ans *= comb(v + (n - 1), v)
    ans %= MOD
print(ans)


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


def get_factors(n):
    """
    素因数分解
    :param int n:
    :type: list of int
    """
    if n <= 1:
        return []

    ret = []
    while n > 2 and n % 2 == 0:
        ret.append(2)
        n //= 2
    i = 3
    while i <= math.sqrt(n):
        if n % i == 0:
            ret.append(i)
            n //= i
        else:
            i += 2
    ret.append(n)
    return ret


def comb(n, r):
    """
    組み合わせの数 nCr
    :param n:
    :param r:
    :return:
    """
    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())
MOD = 10 ** 9 + 7

# divs = sorted(get_divisors(m))
# # dp[d]: 累積積が d となる数列の数
# dp = {d: 1 for d in divs}
# for _ in range(n - 1):
#     for i in reversed(range(len(divs))):
#         div = divs[i]
#         dp[div] = sum([dp[d] for d in divs if div % d == 0]) % MOD
#     print(dp)
# print(dp)
# おそい


factors = get_factors(m)
counts = Counter(factors)
# k**v を全部かけあわせたやつが m に一致する
# print(functools.reduce(operator.mul, [k ** v for k, v in counts.items()]))

# v 個の k を n 個の数に配分する組み合わせの数
# → v + (n-1) 個のスペースへの v の置き方の組み合わせの数
ans = 1
for k, v in counts.items():
    ans *= comb(v + (n - 1), v)
    ans %= MOD
print(ans)

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


def get_divisors(n):
    """
    n の約数をリストで返す
    :param int n:
    :return:
    """
    ret = []
    for i in range(1, int(math.sqrt(n)) + 1):
        if n % i == 0:
            ret.append(i)
            if n // i != i:
                ret.append(n // i)
    return ret


def get_factors(n):
    """
    素因数分解
    :param int n:
    :type: list of int
    """
    ret = []
    i = 2
    while 2 <= i <= n:
        if n % i == 0:
            ret.append(i)
            n //= i
        else:
            i += 1
    return ret


def comb(n, r):
    """
    組み合わせの数 nCr
    :param n:
    :param r:
    :return:
    """
    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())
MOD = 10 ** 9 + 7

# divs = sorted(get_divisors(m))
# # dp[d]: 累積積が d となる数列の数
# dp = {d: 1 for d in divs}
# for _ in range(n - 1):
#     for i in reversed(range(len(divs))):
#         div = divs[i]
#         dp[div] = sum([dp[d] for d in divs if div % d == 0]) % MOD
#     print(dp)
# print(dp)
# おそい


factors = get_factors(m)
counts = Counter(factors)
# k**v を全部かけあわせたやつが m に一致する
# print(functools.reduce(operator.mul, [k ** v for k, v in counts.items()]))

# v 個の k を n 個の数に配分する組み合わせの数
# → v + (n-1) 個のスペースへの v の置き方の組み合わせの数
ans = 1
for k, v in counts.items():
    ans *= comb(v + (n - 1), v)
    ans %= MOD
print(ans)


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


def get_factors(n):
    """
    素因数分解
    :param int n:
    :type: list of int
    """
    if n <= 1:
        return []

    ret = []
    while n > 2 and n % 2 == 0:
        ret.append(2)
        n //= 2
    i = 3
    while i <= math.sqrt(n):
        if n % i == 0:
            ret.append(i)
            n //= i
        else:
            i += 2
    ret.append(n)
    return ret


def comb(n, r):
    """
    組み合わせの数 nCr
    :param n:
    :param r:
    :return:
    """
    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())
MOD = 10 ** 9 + 7

# divs = sorted(get_divisors(m))
# # dp[d]: 累積積が d となる数列の数
# dp = {d: 1 for d in divs}
# for _ in range(n - 1):
#     for i in reversed(range(len(divs))):
#         div = divs[i]
#         dp[div] = sum([dp[d] for d in divs if div % d == 0]) % MOD
#     print(dp)
# print(dp)
# おそい


factors = get_factors(m)
counts = Counter(factors)
# k**v を全部かけあわせたやつが m に一致する
# print(functools.reduce(operator.mul, [k ** v for k, v in counts.items()]))

# v 個の k を n 個の数に配分する組み合わせの数
# → v + (n-1) 個のスペースへの v の置き方の組み合わせの数
ans = 1
for k, v in counts.items():
    ans *= comb(v + (n - 1), v)
    ans %= MOD
print(ans)

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

from scipy.misc import comb


def get_divisors(n):
    """
    n の約数をリストで返す
    :param int n:
    :return:
    """
    ret = []
    for i in range(1, int(math.sqrt(n)) + 1):
        if n % i == 0:
            ret.append(i)
            if n // i != i:
                ret.append(n // i)
    return ret


def get_factors(n):
    """
    素因数分解
    :param int n:
    :type: list of int
    """
    ret = []
    i = 2
    while 2 <= i <= n:
        if n % i == 0:
            ret.append(i)
            n //= i
        else:
            i += 1
    return ret


n, m = map(int, input().split())
MOD = 10 ** 9 + 7

# divs = sorted(get_divisors(m))
# # dp[d]: 累積積が d となる数列の数
# dp = {d: 1 for d in divs}
# for _ in range(n - 1):
#     for i in reversed(range(len(divs))):
#         div = divs[i]
#         dp[div] = sum([dp[d] for d in divs if div % d == 0]) % MOD
#     print(dp)
# print(dp)
# おそい


factors = get_factors(m)
counts = Counter(factors)
# k**v を全部かけあわせたやつが m に一致する
# print(functools.reduce(operator.mul, [k ** v for k, v in counts.items()]))

# v 個の k を n 個の数に配分する組み合わせの数
# → v + (n-1) 個のスペースへの v の置き方の組み合わせの数
ans = 1
for k, v in counts.items():
    ans *= comb(v + (n - 1), v, exact=True)
    ans %= MOD
print(ans)


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


def get_factors(n):
    """
    素因数分解
    :param int n:
    :type: list of int
    """
    if n <= 1:
        return []

    ret = []
    while n > 2 and n % 2 == 0:
        ret.append(2)
        n //= 2
    i = 3
    while i <= math.sqrt(n):
        if n % i == 0:
            ret.append(i)
            n //= i
        else:
            i += 2
    ret.append(n)
    return ret


def comb(n, r):
    """
    組み合わせの数 nCr
    :param n:
    :param r:
    :return:
    """
    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())
MOD = 10 ** 9 + 7

# divs = sorted(get_divisors(m))
# # dp[d]: 累積積が d となる数列の数
# dp = {d: 1 for d in divs}
# for _ in range(n - 1):
#     for i in reversed(range(len(divs))):
#         div = divs[i]
#         dp[div] = sum([dp[d] for d in divs if div % d == 0]) % MOD
#     print(dp)
# print(dp)
# おそい


factors = get_factors(m)
counts = Counter(factors)
# k**v を全部かけあわせたやつが m に一致する
# print(functools.reduce(operator.mul, [k ** v for k, v in counts.items()]))

# v 個の k を n 個の数に配分する組み合わせの数
# → v + (n-1) 個のスペースへの v の置き方の組み合わせの数
ans = 1
for k, v in counts.items():
    ans *= comb(v + (n - 1), v)
    ans %= MOD
print(ans)