Buggy python submission (verdict: Runtime Error):
"""
8:30:00
"""

from collections import defaultdict
def getprime(n):
    if not isinstance(n, int):
        raise TypeError("Input int")
    if n < 2:
        raise ValueError("N >= 2")
    prime = []
    # 約数はsqrt(N)まで調べればOK
    data = [i+1 for i in range(1,n)]
    while True:
        p = data[0]
        if p >= int(n**0.5):
            return prime+data
        prime.append(p)
        # pで割り切れないものだけを残す
        data = [d for d in data if d%p != 0]

def factorization(n):
    factors = defaultdict(int)
    primes = getprime(int(n**0.5))
    for prime in primes:
        while n % prime == 0:
            factors[prime] += 1
            n //= prime
            # print(factors,n)
    if n != 1:
        factors[n] += 1
    return factors


def modconb(n,k,mod):
    # テーブルを作る
    fac = [0]*(n+1)
    finv = [0]*(n+1)
    inv = [0]*(n+1)  

    fac[0] = fac[1] = 1
    finv[0] = finv[1] = 1
    inv[1] = 1

    for i in range(2,n+1):
        fac[i] = fac[i-1]*i % mod
        inv[i] = mod - inv[mod%i] * (mod//i) % mod
        finv[i] = finv[i-1] * inv[i] % mod

    if n<k: return 0
    if n<0 or k<0: return 0
    return(fac[n]*(finv[k]*finv[n-k]%mod)%mod)

"""
1 * 1 * 1のどこに素因数をかけるか
3^3だとして
どこかで3回3をかけないといけない
a + b + c = 3 //重複組合せ
3*3-1C3
こいつをかけ合わせると答えになる
modconbいる
"""

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

factors = factorization(m)
ans = 1
for k in factors.keys():
    x = factors[k]
    ans *= modconb(x+n-1,x,mod)
    ans %= mod
print(ans)


Fixed submission:
from math import factorial
N, M = map(int,input().split())

# 素因数分解(小さい方から順に割っていく。sqrt(2)まで)
def factorize(n):
    i = 2
    table = [0]
    cnt= [0]
    while i * i <= n:
        while n % i == 0:
            n /= i
            if table[-1] != i:
                table.append(i)
                cnt.append(0)
            cnt[-1] += 1
        i += 1
    if n > 1:
        table.append(n)
        cnt.append(1)
    return table,cnt


fs,ns = factorize(M)
ans = 1
for n in ns[1:]:
    a = 1
    for i in range(N,n+N):
        a *= i
    ans *= a//factorial(n)
print(ans%(10**9+7))

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

# 素因数分解(小さい方から順に割っていく。sqrt(2)まで)
def factorize(n):
    i = 2
    table = [0]
    cnt= [0]
    while i * i <= n:
        while n % i == 0:
            n /= i
            if table[-1] != i:
                table.append(i)
                cnt.append(0)
            cnt[-1] += 1
        i += 1
    if n > 1:
        table.append(n)
        cnt.append(1)
    return table,cnt

# 組み合わせ
def combination(N,M):
    return factorial(N)//(factorial(M)*factorial(N-M))

fs,ns = factorize(M)
ans = 1
for n in ns[1:]:
    ans *= combination(n+N-1,n)
print(ans%(10**9+7))

Fixed submission:
from math import factorial
N, M = map(int,input().split())

# 素因数分解(小さい方から順に割っていく。sqrt(2)まで)
def factorize(n):
    i = 2
    table = [0]
    cnt= [0]
    while i * i <= n:
        while n % i == 0:
            n /= i
            if table[-1] != i:
                table.append(i)
                cnt.append(0)
            cnt[-1] += 1
        i += 1
    if n > 1:
        table.append(n)
        cnt.append(1)
    return table,cnt


fs,ns = factorize(M)
ans = 1
for n in ns[1:]:
    a = 1
    for i in range(N,n+N):
        a *= i
    ans *= a//factorial(n)
print(ans%(10**9+7))

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

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

# 素因数分解(小さい方から順に割っていく。sqrt(2)まで)
def factorize(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

# 組み合わせ
def combination(N,M):
    return factorial(N)//(factorial(M)*factorial(N-M))

fs = factorize(M)
fset = list(set(fs))
ans = 1
for f in fset:
    cnt = fs.count(f)
    ans *= combination(cnt+N-1,cnt)
print(ans%(10**9+7))


Fixed submission:
from math import factorial
N, M = map(int,input().split())

# 素因数分解(小さい方から順に割っていく。sqrt(2)まで)
def factorize(n):
    i = 2
    table = [0]
    cnt= [0]
    while i * i <= n:
        while n % i == 0:
            n /= i
            if table[-1] != i:
                table.append(i)
                cnt.append(0)
            cnt[-1] += 1
        i += 1
    if n > 1:
        table.append(n)
        cnt.append(1)
    return table,cnt


fs,ns = factorize(M)
ans = 1
for n in ns[1:]:
    a = 1
    for i in range(N,n+N):
        a *= i
    ans *= a//factorial(n)
print(ans%(10**9+7))

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

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

# N,M = 100000,10**9-3
# 素因数分解(小さい方から順に割っていく)
def factorize(n):
    b = 2
    fct = []
    while b * b <= n:
        while n % b == 0:
            n //= b
            fct.append(b)
        b = b + 1
    if n > 1:
        fct.append(n)
    return fct

# 組み合わせ
def combination(N,M):
    return factorial(N)//(factorial(M)*factorial(N-M))

fs = factorize(M)
fset = list(set(fs))
ans = 1
for f in fset:
    cnt = fs.count(f)
    ans *= combination(cnt+N-1,cnt)
print(ans%(10**9+7))

Fixed submission:
from math import factorial
N, M = map(int,input().split())

# 素因数分解(小さい方から順に割っていく。sqrt(2)まで)
def factorize(n):
    i = 2
    table = [0]
    cnt= [0]
    while i * i <= n:
        while n % i == 0:
            n /= i
            if table[-1] != i:
                table.append(i)
                cnt.append(0)
            cnt[-1] += 1
        i += 1
    if n > 1:
        table.append(n)
        cnt.append(1)
    return table,cnt


fs,ns = factorize(M)
ans = 1
for n in ns[1:]:
    a = 1
    for i in range(N,n+N):
        a *= i
    ans *= a//factorial(n)
print(ans%(10**9+7))