Buggy python submission (verdict: Time Limit Exceeded):
import math
def factorize(m):
    fct = []
    b = 2
    while b * b <= m:
        cnt = 0
        while m % b == 0:
            m //= b
            cnt += 1
        if b > 0:
            fct.append([b, cnt])
        b += 1 
    if m > 1:
        fct.append([m, 1])
    return fct

def comb(n, r):
    if n < r or n < 0 or r < 0:
        return 0
    else:
        return math.factorial(n)//(math.factorial(n-r)*math.factorial(r))

N, M = map(int, input().split())
ans = 1
M_fct = factorize(M)

for mf in M_fct:
    #mf[1]個をN通りに分ける→comb(mf[1]+N-1,mf[1])
    ans *= comb(N + mf[1] - 1, mf[1])
print(ans% (10 ** 9 + 7))

Fixed submission:
import math
def factorize(m):
    fct = []
    b = 2
    while b * b <= m:
        cnt = 0
        while m % b == 0:
            m //= b
            cnt += 1
        if cnt > 0:
            fct.append(cnt)
        b += 1
    if m > 1:
        fct.append(1)
    return fct

def comb(n, r):
    if n < r or n < 0 or r < 0:
        return 0
    else:
        return math.factorial(n)//(math.factorial(n-r)*math.factorial(r))

N, M = map(int, input().split())
ans = 1
M_fct = factorize(M)

for mf in M_fct:
    #mf[1]個をN通りに分ける→comb(mf[1]+N-1,mf[1])
    ans *= comb(N + mf - 1, mf)
    ans %= 10**9+7
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import math
def factorize(m):
    fct = []
    b = 2
    while b * b <= m:
        cnt = 0
        while m % b == 0:
            m //= b
            cnt += 1
        if b > 0:
            fct.append([b, cnt])
        b += 1 
    if m > 1:
        fct.append([m, 1])
    return fct

def comb(n, r):
    if n < r or n < 0 or r < 0:
        return 0
    else:
        return math.factorial(n)//(math.factorial(n-r)*math.factorial(r))

N, M = map(int, input().split())
ans = 1
M_fct = factorize(M)

for mf in M_fct:
    #mf[1]個をN通りに分ける→comb(mf[1]+N-1,mf[1])
    ans *= comb(N + mf[1] - 1, mf[1])
print(ans% (10 ** 9 + 7))

Fixed submission:
import math
def factorize(m):
    fct = []
    b = 2
    while b * b <= m:
        cnt = 0
        while m % b == 0:
            m //= b
            cnt += 1
        if cnt > 0:
            fct.append(cnt)
        b += 1
    if m > 1:
        fct.append(1)
    return fct

def comb(n, r):
    if n < r or n < 0 or r < 0:
        return 0
    else:
        return math.factorial(n)//(math.factorial(n-r)*math.factorial(r))

N, M = map(int, input().split())
ans = 1
M_fct = factorize(M)

for mf in M_fct:
    #mf[1]個をN通りに分ける→comb(mf[1]+N-1,mf[1])
    ans *= comb(N + mf - 1, mf)
    ans %= 10**9+7
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import math
import collections
def factorize(m):
    b = 2
    fct = []
    while b * b <= m:
        while m % b == 0:
            m //= b
            fct.append(b)
        b += 1
    if m > 1:
        fct.append(m)
    return fct

def comb(n, r):
    if n < r or n < 0 or r < 0:
        return 0
    else:
        return math.factorial(n)//(math.factorial(n-r)*math.factorial(r))

N, M = map(int, input().split())
ans = 1
M_fact = factorize(M)
c = collections.Counter(M_fact)

for ci in c.values():
    #i個をN通りに分ける→i+N-1,i
    ans *= comb(N+ci-1,ci)
print(ans%(10**9+7))

Fixed submission:
import math
def factorize(m):
    fct = []
    b = 2
    while b * b <= m:
        cnt = 0
        while m % b == 0:
            m //= b
            cnt += 1
        if cnt > 0:
            fct.append(cnt)
        b += 1
    if m > 1:
        fct.append(1)
    return fct

def comb(n, r):
    if n < r or n < 0 or r < 0:
        return 0
    else:
        return math.factorial(n)//(math.factorial(n-r)*math.factorial(r))

N, M = map(int, input().split())
ans = 1
M_fct = factorize(M)

for mf in M_fct:
    #mf[1]個をN通りに分ける→comb(mf[1]+N-1,mf[1])
    ans *= comb(N + mf - 1, mf)
    ans %= 10**9+7
print(ans)

Buggy python submission (verdict: Runtime Error):
import math
def factorize(m):
    b = 2
    fct = [0]*(10**5)
    while b * b <= m:
        while m % b == 0:
            m //= b
            fct[b] +=1
        b = b + 1
    if m > 1:
        fct[m]+=1
    return fct

def comb(n, r):
    if n < r or n < 0 or r < 0:
        return 0
    else:
        return math.factorial(n)//(math.factorial(n-r)*math.factorial(r))

N, M = map(int, input().split())
ans = 1
M_fact = factorize(M)

for i in M_fact:
    if i != 0: #i個をN通りに分ける→i+N-1,i
        ans *= comb(N+i-1,i)
print(ans%(10**9+7))

Fixed submission:
import math
def factorize(m):
    fct = []
    b = 2
    while b * b <= m:
        cnt = 0
        while m % b == 0:
            m //= b
            cnt += 1
        if cnt > 0:
            fct.append(cnt)
        b += 1
    if m > 1:
        fct.append(1)
    return fct

def comb(n, r):
    if n < r or n < 0 or r < 0:
        return 0
    else:
        return math.factorial(n)//(math.factorial(n-r)*math.factorial(r))

N, M = map(int, input().split())
ans = 1
M_fct = factorize(M)

for mf in M_fct:
    #mf[1]個をN通りに分ける→comb(mf[1]+N-1,mf[1])
    ans *= comb(N + mf - 1, mf)
    ans %= 10**9+7
print(ans)