Buggy python submission (verdict: Runtime Error):
import math
import sys
input = sys.stdin.readline

def main():
    N,M = map(int,input().split())
    div_list = []
    d = 2
    ans = 1
    MOD = 10**9+7
    while M != 1:
        count = 0
        while M%d == 0:
            count += 1
            M //= d
        div_list.append(count)
        d += 1
    _m = max(div_list)
    fac = [1]
    for i in range(1,_m+N):
        fac.append(fac[-1]*i%MOD)
    use = max(N-1,_m)
    
    def power(x,y):
        if y == 0:return 1
        elif y == 1:return x%MOD
        elif y%2 == 0:return power(x,y//2)**2%MOD
        else:return power(x,y//2)**2*x%MOD
        
    invfac = [0 for _ in range(use+1)]
    invfac[-1] = power(fac[use],MOD-2)
    for i in range(use-1,-1,-1):
        invfac[i] = invfac[i+1]*(i+1)%MOD
        
    for i in div_list:
        a = fac[i+N-1]
        b = invfac[i]
        c = invfac[N-1]
        ans *= (a*b*c)%MOD
        
    print(ans%MOD)

if __name__ == "__main__":
    main()


Fixed submission:
import sys
input = sys.stdin.buffer.readline
from collections import defaultdict
import copy

def main():
    N,M = map(int,input().split())
    d = defaultdict(int)
    MOD = 10**9+7
    R = 10**5+100
    fac = [0 for _ in range(R+1)]
    fac[0],fac[1] = 1,1
    inv = copy.deepcopy(fac)
    invfac = copy.deepcopy(fac)
    
    for i in range(2,R+1):
        fac[i] = (fac[i-1]*i)%MOD
        inv[i] = MOD-(MOD//i)*inv[MOD%i]%MOD
        invfac[i] = (invfac[i-1]*inv[i])%MOD
        
    def coef(x,y):
        num = (((fac[x+y]*invfac[y])%MOD)*invfac[x]%MOD)
        return num

    while M%2 == 0:
        d[2] += 1
        M //= 2
    f = 3
    while f ** 2 <= M:
        if M % f == 0:
            d[f] += 1
            M //= f
        else:
            f += 2
    if M != 1:
        d[M] += 1
    
    l = list(d.values())
    ans = 1
    for num in l:
        ans *= coef(num,N-1)
        ans %= MOD
        
    print(ans)
    
if __name__ == "__main__":
    main()

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

def main():
    N,M = map(int,input().split())
    div_list = []
    d = 2
    ans = 1
    while M != 1:
        count = 0
        while M%d == 0:
            count += 1
            M //= d
        div_list.append(count)
        d += 1
    for i in div_list:
        a = math.factorial(i+N-1)
        b = math.factorial(i)
        c = math.factorial(N-1)
        ans *= (a//(b*c))%(10**9+7)
    print(ans%(10**9+7))

if __name__ == "__main__":
    main()

Fixed submission:
import sys
input = sys.stdin.buffer.readline
from collections import defaultdict
import copy

def main():
    N,M = map(int,input().split())
    d = defaultdict(int)
    MOD = 10**9+7
    R = 10**5+100
    fac = [0 for _ in range(R+1)]
    fac[0],fac[1] = 1,1
    inv = copy.deepcopy(fac)
    invfac = copy.deepcopy(fac)
    
    for i in range(2,R+1):
        fac[i] = (fac[i-1]*i)%MOD
        inv[i] = MOD-(MOD//i)*inv[MOD%i]%MOD
        invfac[i] = (invfac[i-1]*inv[i])%MOD
        
    def coef(x,y):
        num = (((fac[x+y]*invfac[y])%MOD)*invfac[x]%MOD)
        return num

    while M%2 == 0:
        d[2] += 1
        M //= 2
    f = 3
    while f ** 2 <= M:
        if M % f == 0:
            d[f] += 1
            M //= f
        else:
            f += 2
    if M != 1:
        d[M] += 1
    
    l = list(d.values())
    ans = 1
    for num in l:
        ans *= coef(num,N-1)
        ans %= MOD
        
    print(ans)
    
if __name__ == "__main__":
    main()