Buggy python submission (verdict: Runtime Error):
from collections import defaultdict as dd

N, M = map(int, input().split())
MOD = 10 ** 9 + 7
# a1 x a2 x .. x aN = M となる数列{ai}が何通りあるか
# まずは素因数分解
def make_prime_dict(x):
    primes = dd(int)
    check = 2
    while True:
        if x % check == 0:
            primes[check] += 1
            x = x // check
        else:
            check += 1
            if check > x:
                break
    return dict(primes)

primes = make_prime_dict(M)

Q = max(primes.values())
fact = [1]
fact_inv = [1]
for i in range(Q+N):
    new_fact = fact[-1] * (i+1) % MOD
    fact.append(new_fact)
    fact_inv.append(pow(new_fact, MOD - 2, MOD))

def mod_comb(n, r, mod):
    return fact[n] * fact_inv[n - r] % mod * fact_inv[r] % mod

res = 1
for q in primes.values():
    res *= mod_comb(q + N - 1, q, MOD)
    res %= MOD

print(res)

Fixed submission:
from collections import defaultdict as dd

N, M = map(int, input().split())
MOD = 10 ** 9 + 7
# a1 x a2 x .. x aN = M となる数列{ai}が何通りあるか
# まずは素因数分解
def make_prime_dict(x):
    primes = dd(int)
    check = 2
    while True:
        if x % check == 0:
            primes[check] += 1
            x = x // check
        else:
            check += 1
            if check > x:
                break
    return dict(primes)

primes = make_prime_dict(M)
if len(primes) == 0:
    print(1)
    exit()
Q = max(primes.values())
fact = [1]
fact_inv = [1]
for i in range(Q+N):
    new_fact = fact[-1] * (i+1) % MOD
    fact.append(new_fact)
    fact_inv.append(pow(new_fact, MOD - 2, MOD))

def mod_comb(n, r, mod):
    return fact[n] * fact_inv[n - r] % mod * fact_inv[r] % mod

res = 1
for q in primes.values():
    res *= mod_comb(q + N - 1, q, MOD)
    res %= MOD

print(res)

Buggy python submission (verdict: Runtime Error):
from collections import defaultdict as dd

N, M = map(int, input().split())
MOD = 10 ** 9 + 7
# a1 x a2 x .. x aN = M となる数列{ai}が何通りあるか
# まずは素因数分解
def make_prime_dict(x):
    primes = dd(int)
    check = 2
    while True:
        if x % check == 0:
            primes[check] += 1
            x = x // check
        else:
            check += 1
            if check > x:
                break
    return dict(primes)

primes = make_prime_dict(M)

Q = max(primes.values())
fact = [1]
fact_inv = [1]
for i in range(Q+N):
    new_fact = fact[-1] * (i+1) % MOD
    fact.append(new_fact)
    fact_inv.append(pow(new_fact, MOD - 2, MOD))

def mod_comb(n, r, mod):
    return fact[n] * fact_inv[n - r] % mod * fact_inv[r] % mod

res = 1
for q in primes.values():
    res *= mod_comb(q + N - 1, q, MOD)
    res %= MOD

print(res)
print(primes)

Fixed submission:
from collections import defaultdict as dd

N, M = map(int, input().split())
MOD = 10 ** 9 + 7
# a1 x a2 x .. x aN = M となる数列{ai}が何通りあるか
# まずは素因数分解
def make_prime_dict(x):
    primes = dd(int)
    check = 2
    while True:
        if x % check == 0:
            primes[check] += 1
            x = x // check
        else:
            check += 1
            if check > x:
                break
    return dict(primes)

primes = make_prime_dict(M)
if len(primes) == 0:
    print(1)
    exit()
Q = max(primes.values())
fact = [1]
fact_inv = [1]
for i in range(Q+N):
    new_fact = fact[-1] * (i+1) % MOD
    fact.append(new_fact)
    fact_inv.append(pow(new_fact, MOD - 2, MOD))

def mod_comb(n, r, mod):
    return fact[n] * fact_inv[n - r] % mod * fact_inv[r] % mod

res = 1
for q in primes.values():
    res *= mod_comb(q + N - 1, q, MOD)
    res %= MOD

print(res)

Buggy python submission (verdict: Runtime Error):
from collections import defaultdict as dd

N, M = map(int, input().split())
MOD = 10 ** 9 + 7
# a1 x a2 x .. x aN = M となる数列{ai}が何通りあるか
# まずは素因数分解
def make_prime_dict(x):
    primes = dd(int)
    check = 2
    while True:
        if x % check == 0:
            primes[check] += 1
            x = x // check
        else:
            check += 1
            if check > x:
                break
    return dict(primes)

primes = make_prime_dict(M)

Q = max(primes.values())
fact = [1]
fact_inv = [1]
for i in range(Q+N):
    new_fact = fact[-1] * (i+1) % MOD
    fact.append(new_fact)
    fact_inv.append(pow(new_fact, MOD - 2, MOD))

def mod_comb(n, r, mod):
    return fact[n] * fact_inv[n - r] % mod * fact_inv[r] % mod

res = 1
for q in primes.values():
    res *= mod_comb(q + N - 1, q, MOD) % MOD

print(res)

Fixed submission:
from collections import defaultdict as dd

N, M = map(int, input().split())
MOD = 10 ** 9 + 7
# a1 x a2 x .. x aN = M となる数列{ai}が何通りあるか
# まずは素因数分解
def make_prime_dict(x):
    primes = dd(int)
    check = 2
    while True:
        if x % check == 0:
            primes[check] += 1
            x = x // check
        else:
            check += 1
            if check > x:
                break
    return dict(primes)

primes = make_prime_dict(M)
if len(primes) == 0:
    print(1)
    exit()
Q = max(primes.values())
fact = [1]
fact_inv = [1]
for i in range(Q+N):
    new_fact = fact[-1] * (i+1) % MOD
    fact.append(new_fact)
    fact_inv.append(pow(new_fact, MOD - 2, MOD))

def mod_comb(n, r, mod):
    return fact[n] * fact_inv[n - r] % mod * fact_inv[r] % mod

res = 1
for q in primes.values():
    res *= mod_comb(q + N - 1, q, MOD)
    res %= MOD

print(res)

Buggy python submission (verdict: Runtime Error):
from collections import defaultdict as dd

N, M = map(int, input().split())
MOD = 10 ** 9 + 7
# a1 x a2 x .. x aN = M となる数列{ai}が何通りあるか
# まずは素因数分解
def make_prime_dict(x):
    primes = dd(int)
    check = 2
    while True:
        if x % check == 0:
            primes[check] += 1
            x = x // check
        else:
            check += 1
            if check > x:
                break
    return dict(primes)

primes = make_prime_dict(M)

fact = [1]
fact_inv = [1]
Q = max(primes.values())
for i in range(1, Q + N):
    fact.append(fact[-1] * i % MOD)
    fact_inv.append(fact_inv[-1] * pow(i, MOD - 2, MOD))

def mod_comb(n, r, mod):
    return fact[n] * fact_inv[n - r] % mod * fact_inv[r] % mod

res = 1
for q in primes.values():
    res *= mod_comb(q + N - 1, q, MOD) % MOD

print(res)

Fixed submission:
from collections import defaultdict as dd

N, M = map(int, input().split())
MOD = 10 ** 9 + 7
# a1 x a2 x .. x aN = M となる数列{ai}が何通りあるか
# まずは素因数分解
def make_prime_dict(x):
    primes = dd(int)
    check = 2
    while True:
        if x % check == 0:
            primes[check] += 1
            x = x // check
        else:
            check += 1
            if check > x:
                break
    return dict(primes)

primes = make_prime_dict(M)
if len(primes) == 0:
    print(1)
    exit()
Q = max(primes.values())
fact = [1]
fact_inv = [1]
for i in range(Q+N):
    new_fact = fact[-1] * (i+1) % MOD
    fact.append(new_fact)
    fact_inv.append(pow(new_fact, MOD - 2, MOD))

def mod_comb(n, r, mod):
    return fact[n] * fact_inv[n - r] % mod * fact_inv[r] % mod

res = 1
for q in primes.values():
    res *= mod_comb(q + N - 1, q, MOD)
    res %= MOD

print(res)