Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(100000)

n, m = map(int, input().split())

MOD = 10 ** 9 + 7

if m == 1:
    print('1')
    exit()

factor = []
temp = 0
x = 2
while m > 1:
    if m % x == 0:
        m //= x
        temp += 1
    elif temp > 0:
        factor.append(temp)
        temp = 0
        x += 1
    else:
        x += 1
factor.append(temp)

nCr = {}
def cmb(n, r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n;
    if (n, r) in nCr: return nCr[(n, r)]

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p;
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    nCr[(n, r)] = result
    return result;

ans = 1
for x in factor:
    ans *= cmb(x + n - 1, n - 1)
    ans %= MOD

print(ans)

Fixed submission:
n, m = map(int, input().split())

MOD = 10 ** 9 + 7

if m == 1:
    print('1')
    exit()

factor = []
temp = 0
x = 2
while m > 1:
    if m % x == 0:
        m //= x
        temp += 1
    elif temp > 0:
        factor.append(temp)
        temp = 0
        x += 1
    else:
        x += 1
factor.append(temp)

nCr = {}
def cmb(n, r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n;
    if (n, r) in nCr: return nCr[(n, r)]

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p;
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    nCr[(n, r)] = result
    return result;

ans = 1
for x in factor:
    ans *= cmb(x + n - 1, n - 1)
    ans %= MOD

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
n, m = map(int, input().split())

MOD = 10 ** 9 + 7

if m == 1:
    print('1')
    exit()

factor = []
temp = 0
x = 2
while m > 1:
    if m % x == 0:
        m //= x
        temp += 1
    elif temp > 0:
        factor.append(temp)
        temp = 0
        x += 1
    else:
        x += 1
factor.append(temp)

def cmb(n, r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n;

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p;
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    return result;

ans = 1
for x in factor:
    ans *= cmb(x + n - 1, n - 1)
    ans %= MOD

print(ans)

Fixed submission:
n, m = map(int, input().split())

MOD = 10 ** 9 + 7

if m == 1:
    print('1')
    exit()

factor = []
temp = 0
x = 2
while m > 1:
    if m % x == 0:
        m //= x
        temp += 1
    elif temp > 0:
        factor.append(temp)
        temp = 0
        x += 1
    else:
        x += 1
factor.append(temp)

nCr = {}
def cmb(n, r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n;
    if (n, r) in nCr: return nCr[(n, r)]

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p;
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    nCr[(n, r)] = result
    return result;

ans = 1
for x in factor:
    ans *= cmb(x + n - 1, n - 1)
    ans %= MOD

print(ans)