Buggy python submission (verdict: Time Limit Exceeded):
N, M = map(int, input().split())
bigp = 10**9+7
L1 = []
L2 = []
p = 2
K = M
while K != 1:
    if K%p == 0:
        L1.append(p)
        K = K//p
        if p not in L2:
            L2.append(p)
    else:
        if p == 2:
            p += 1
        else:
            p += 2

ans = 1
def ModComb(n, r, p):
    N = n%p
    R = r%p
    if N<R:
        return 0
    if N < 2*R:
        R = N-R
    if R == 0:
        return 1
    else:
        return (n*pow(r, p-2, p))%p*ModComb(n-1, r-1, p)


for x in L2:
    primepower = L1.count(x)
    ans *= ModComb(N+primepower-1, primepower, bigp)
    ans %= bigp

print(ans)


Fixed submission:
N, M = map(int, input().split())
bigp = 10**9+7
L = []
p, power = 2, 0
K = M
while p*p <= K:
    while K%p == 0:
        K = K//p
        power += 1
    if power > 0:
        L.append([p, power])
    if p == 2:
        p += 1
    else:
        p += 2
    power = 0
if K > 1:
    L.append([K, 1])


ans = 1
def ModComb(n, r, p):
    N = n%p
    R = r%p
    if N<R:
        return 0
    if N < 2*R:
        R = N-R
    if R == 0:
        return 1
    else:
        return (n*pow(r, p-2, p))%p*ModComb(n-1, r-1, p)


for i in range(len(L)):
    power = L[i][1]
    ans *= ModComb(N+power-1, power, bigp)
    ans %= bigp

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
N, M = map(int, input().split())
bigp = 10**9+7
L1 = []
L2 = []
p = 2
K = M
while K != 1:
    if K%p == 0:
        L1.append(p)
        K = K//p
        if p not in L2:
            L2.append(p)
    else:
        p = p+1

ans = 1
def ModComb(n, r, p):
    N = n%p
    R = r%p
    if N<R:
        return 0
    if N < 2*R:
        R = N-R
    if R == 0:
        return 1
    else:
        return (n*pow(r, p-2, p))%p*ModComb(n-1, r-1, p)


for x in L2:
    primepower = L1.count(x)
    ans *= ModComb(N+primepower-1, primepower, bigp)%bigp

print(ans%bigp)


Fixed submission:
N, M = map(int, input().split())
bigp = 10**9+7
L = []
p, power = 2, 0
K = M
while p*p <= K:
    while K%p == 0:
        K = K//p
        power += 1
    if power > 0:
        L.append([p, power])
    if p == 2:
        p += 1
    else:
        p += 2
    power = 0
if K > 1:
    L.append([K, 1])


ans = 1
def ModComb(n, r, p):
    N = n%p
    R = r%p
    if N<R:
        return 0
    if N < 2*R:
        R = N-R
    if R == 0:
        return 1
    else:
        return (n*pow(r, p-2, p))%p*ModComb(n-1, r-1, p)


for i in range(len(L)):
    power = L[i][1]
    ans *= ModComb(N+power-1, power, bigp)
    ans %= bigp

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
N, M = map(int, input().split())
bigp = 10**9+7
L1 = []
L2 = []
p = 2
max = M
K = M
while p <= max:
    if K%p == 0:
        L1.append(p)
        K = K//p
        if p not in L2:
            L2.append(p)
    else:
        p = p+1

ans = 1
def ModComb(n, r, p):
    N = n%p
    R = r%p
    if N<R:
        return 0
    if N < 2*R:
        R = N-R
    if R == 0:
        return 1
    else:
        return (n*pow(r, p-2, p))%p*ModComb(n-1, r-1, p)


for x in L2:
    primepower = L1.count(x)
    ans *= ModComb(N+primepower-1, primepower, bigp)%bigp

print(ans%bigp)

Fixed submission:
N, M = map(int, input().split())
bigp = 10**9+7
L = []
p, power = 2, 0
K = M
while p*p <= K:
    while K%p == 0:
        K = K//p
        power += 1
    if power > 0:
        L.append([p, power])
    if p == 2:
        p += 1
    else:
        p += 2
    power = 0
if K > 1:
    L.append([K, 1])


ans = 1
def ModComb(n, r, p):
    N = n%p
    R = r%p
    if N<R:
        return 0
    if N < 2*R:
        R = N-R
    if R == 0:
        return 1
    else:
        return (n*pow(r, p-2, p))%p*ModComb(n-1, r-1, p)


for i in range(len(L)):
    power = L[i][1]
    ans *= ModComb(N+power-1, power, bigp)
    ans %= bigp

print(ans)