qyliang/CodeNanoFix huggingface dataset:
Buggy code:
n, m = map(int, input().split())
MOD = 1000000007
def comb(x, y):
    ret = 1
    for a in range(x, x - y, -1):
        ret *= a
    for b in range(y, 0, -1):
        ret //= b
    return ret

ans = 1
for i in range(2, 100000):
    if i > m:break
    cnt = 0
    while m % i == 0:
        cnt += 1
        m //= i
    ans *= comb(cnt + n - 1, cnt)
if i != 1:
    ans *= comb(n, 1)

print(ans % MOD)

Fixed code:
n, m = map(int, input().split())
MOD = 1000000007
def comb(x, y):
    ret = 1
    for a in range(x, x - y, -1):
        ret *= a
    for b in range(y, 0, -1):
        ret //= b
    return ret

ans = 1
for i in range(2, 100000):
    if i > m:break
    cnt = 0
    while m % i == 0:
        cnt += 1
        m //= i
    ans *= comb(cnt + n - 1, cnt)
if m != 1:
    ans *= comb(n, 1)

print(ans % MOD)
Buggy code:
def prf(n):
    pf = {}
    for i in range(2, int(n ** 1 / 2) + 1):
        while n % i == 0:
            if not i in pf:
                pf[i] = 0
            pf[i] += 1
            n //= i
    if n > 1:
        pf[n] = 1
    return pf

def comb(n, k):
    k = min(k, n - k)
    result = 1
    for i in range(n, n - k, -1):
        result *= i
    for i in range(1, k + 1):
        result //= i 
    return result

n, m = map(int, input().split())
mod = 10 ** 9 + 7

ans = 1
for i in prf(m).values():
    ans = ans * comb(n - 1 + i, i) % mod
    
print(ans)

Fixed code:
n, m = map(int, input().split())
mod = 10 ** 9 + 7

def prf(n):
    pf = {}
    for i in range(2, int(n**0.5)+1):
        while n % i == 0:
            pf[i] = pf.get(i, 0) + 1
            n //= i
    if n > 1:
        pf[n] = 1
    return pf

def comb(n, k):
    k = min(k, n-k)
    result = 1
    for i in range(n-k+1, n+1):
        result *= i
    for i in range(1, k+1):
        result //= i
    return result

ans = 1
for v in prf(m).values():
    ans = ans * comb(n-1+v, v) % mod
    
print(ans)
Buggy code:
mod = 10 ** 9 + 7
n, m = map(int, input().split())

f = []
p = 2
while p * p <= m:
    if m % p != 0:
        p += 1
        continue
    c = 0
    while m % p == 0:
        c += 1
        m //= p
    f.append(c)
    p += 1
if m != 1:
    f.append(1)


def comb(a, b):
    ret = 1
    r = min(b, a-b)
    for i in range(a-r+1, a+1):
        ret *= i
    for j in range(1, r+1):
        ret /= j
    return (int)(ret)


res = 1
for ele in f:
    ret = comb(ele+n-1, n-1)
    res *= ret

print(res % mod)


Fixed code:
import math
mod = 10 ** 9 + 7
n, m = map(int, input().split())

f = []
p = 2
while p * p <= m:
    if m % p != 0:
        p += 1
        continue
    c = 0
    while m % p == 0:
        c += 1
        m //= p
    f.append(c)
    p += 1
if m != 1:
    f.append(1)


def comb(a, b):
    ret = 1
    r = min(b, a-b)
    for i in range(a-r+1, a+1):
        ret *= i
    for j in range(1, r+1):
        ret //= j

    return (int)(ret)


ans = 1
for i in f:
    ans *= comb(i+n-1, i)
print(ans % mod)
Buggy code:
def prime_factorize(num):
    """
    This function performs prime factorization on the input natural number.
    The result is returned in the form of a dictionary with the prime number as the key
    and its number as the value.
    :param num:
    :return prime_factor: Dictionary with the prime number as the key and its number as the value.
    """
    prime_factor = {}
    i = 2
    while i ** 2 <= num:
        while num % i == 0:
            num //= i
            if i in prime_factor.keys():
                prime_factor[i] += 1
            else:
                prime_factor[i] = 1
        i += 1
    if num > 1:
        prime_factor[num] = 1
    return prime_factor


from math import factorial


def comb(n, r):
    return factorial(n) // (factorial(n-r) * factorial(r))


n, m = map(int, input().split())
r = 1
prime_fac = prime_factorize(m)
print(prime_fac)
for v in prime_fac.values():
    r *= comb(v+n-1, v)
mod = 1000000000 + 7
print(r % mod)


Fixed code:
def prime_factorize(num):
    """
    This function performs prime factorization on the input natural number.
    The result is returned in the form of a dictionary with the prime number as the key
    and its number as the value.
    :param num:
    :return prime_factor: Dictionary with the prime number as the key and its number as the value.
    """
    prime_factor = {}
    i = 2
    while i ** 2 <= num:
        while num % i == 0:
            num //= i
            if i in prime_factor.keys():
                prime_factor[i] += 1
            else:
                prime_factor[i] = 1
        i += 1
    if num > 1:
        prime_factor[num] = 1
    return prime_factor


from math import factorial


def comb(n, r):
    return factorial(n) // (factorial(n-r) * factorial(r))


n, m = map(int, input().split())
r = 1
prime_fac = prime_factorize(m)
for v in prime_fac.values():
    r *= comb(v+n-1, v)
mod = 1000000000 + 7
print(r % mod)
Buggy code:
import collections

def factor(m):
    num=m
    s=[]
    i=2
    while i*i<=m:
        if num%i:
            i+=1
        else:
            s.append(i)
            num//=i
    if num!=1:
        s.append(num)
    return s

def conb(n, r):
	N, R = n, r
	for i in range(1, r):
		N *= n-i
		R *= r-i
	return N // R
	
n,m=map(int,input().split())
a=factor(m)
b=collections.Counter(a)
mod=10**9+7
ans=1
for i in b.values():
    ans=(ans*conb(n+i-1,n-1))%mod
print(ans)

Fixed code:
import collections

def factor(m):
    num=m
    s=[]
    i=2
    while i*i<=m:
        if num%i:
            i+=1
        else:
            s.append(i)
            num//=i
    if num!=1:
        s.append(num)
    return s

def conb(n, r):
	N, R = n, r
	for i in range(1, r):
		N *= n-i
		R *= r-i
	return N // R
	
n,m=map(int,input().split())
a=factor(m)
b=collections.Counter(a)
mod=10**9+7
ans=1
for i in b.values():
    ans=(ans*conb(n+i-1,i))%mod
print(ans)
Buggy code:
import collections

def factor(m):
  q = m
  r = []
  i = 2
  while i * i <= m:
    if q % i:
      i += 1
    else:
      r.append(i)
      q //= i
  return r

n, m = map(int, input().split())
p = 10 ** 9 + 7

r = factor(m)
v = collections.Counter(r)
c = 1
for value in v.values():
  temp = 1
  for i in range(value):
    temp *= value + n - 1 - i
  for i in range(value):
    temp //= i + 1
  temp %= p
  c = c * temp % p
print(c)
  
  
  

Fixed code:
import collections

def factor(m):
  q = m
  r = []
  i = 2
  while i * i <= m:
    if q % i:
      i += 1
    else:
      r.append(i)
      q //= i
  if q != 1:
    r.append(q)
  return r

n, m = map(int, input().split())
p = 10 ** 9 + 7

r = factor(m)
v = collections.Counter(r)
c = 1
for value in v.values():
  temp = 1
  for i in range(value):
    temp *= value + n - 1 - i
  for i in range(value):
    temp //= i + 1
  temp %= p
  c = c * temp % p
print(c)
Buggy code:
import sys
input = sys.stdin.readline

N, M = (int(i) for i in input().split())

def soin(N):
	res = []
	i = 2
	while i < round(N**(1/2)) + 3:
		if N%i == 0:
			res.append(i)
			N = N//i
			i = 2
		else:
			i += 1
	res.append(N)
	return res

def power(a, b):
	if b == 0:
		return 0
	elif b == 1:
		return a % 1000000007
	elif b % 2 == 0:
		return (power(a, b//2) ** 2) % 1000000007
	else:
		return (power(a, b//2) ** 2 * a) % 1000000007

def divide(a, b):
	return (a * power(b, 1000000005)) % 1000000007

def combination(a, b):
	res = 1
	for i in range(b):
		res *= a - i
		res = res % 1000000007
	for i in range(b):
		res = divide(res, i+1)
	return res
	
L = soin(M)
cc = 1
res = 1
for i in range(len(L) -1):
	if L[i] == L[i+1]:
		cc += 1
	else:
		res *= combination(N + cc -1, cc)
		res = res % 1000000007
		cc = 1
res *= combination(N+cc -1, cc)
res = res % 1000000007
print(res)

Fixed code:
import sys
input = sys.stdin.readline

N, M = (int(i) for i in input().split())

def soin(N):
	res = []
	i = 2
	while i < round(N**(1/2)) + 3:
		if N%i == 0:
			res.append(i)
			N = N//i
			i = 2
		else:
			i += 1
	if N != 1:
		res.append(N)
	return res

def power(a, b):
	if b == 0:
		return 0
	elif b == 1:
		return a % 1000000007
	elif b % 2 == 0:
		return (power(a, b//2) ** 2) % 1000000007
	else:
		return (power(a, b//2) ** 2 * a) % 1000000007

def divide(a, b):
	return (a * power(b, 1000000005)) % 1000000007

def combination(a, b):
	res = 1
	for i in range(b):
		res *= a - i
		res = res % 1000000007
	for i in range(b):
		res = divide(res, i+1)
	return res
if M == 1:
	res = 1
else:
	L = soin(M)
	cc = 1
	res = 1
	for i in range(len(L) -1):
		if L[i] == L[i+1]:
			cc += 1
		else:
			res *= combination(N + cc -1, cc)
			res = res % 1000000007
			cc = 1
	res *= combination(N+cc -1, cc)
	res = res % 1000000007
print(res)
Buggy code:
n, m = map(int, input().split())
mod = 10 ** 9 + 7

def prf(n):
    pf = {}
    for i in range(2, int(n**0.5)+1):
        while n % i == 0:
            pf[i] = pf.get(i, 0) + 1
            n //= i
    if n > 1:
        pf[n] = 1
    return pf

def comb(n, k):
    k = min(k, n-k)
    result = 1
    for i in range(n-k+1, n+1):
        result *= i
    for i in range(1, k+1):
        result //= i
    return result

ans = 1
for v in prf(m).values():
    ans *= comb(n-1+v, v) % mod
    
print(ans)

Fixed code:
def prf(m):
    pf = {}
    for i in range(2, int(m**0.5)+1):
        while m % i == 0:
            pf[i] = pf.get(i, 0)+1
            m //= i
    if m > 1:
        pf[m] = 1
    return pf
def inpl(): return [int(i) for i in input().split()]
def comb(n, k):
    k = min(k, n - k)
    result = 1
    for i in range(n, n - k, -1):
        result *= i
    for i in range(1, k + 1):
        result //= i 
    return result

mod = 10**9+7
N, M = inpl()

ans = 1
for i in prf(M).values():
    ans = ans*comb(N+i-1, i)%mod
print(ans)
Buggy code:
from math import *

def Prime_Factorization(M):
    factor_count_list = []

    while True:
        root_M = int(sqrt(M))

        for i in range(2, root_M + 1):
            e = 0
            while M % i == 0:
                e += 1
                M = M // i
            if e > 0:
                factor_count_list.append(e)
                break
            if (M == 1):
                break
        else:
            break
    if M > root_M:
        factor_count_list.append(1)

    print(factor_count_list)
    return factor_count_list

def comb(num_object, num_bar):
    return factorial(num_object) // (factorial(num_object - num_bar) * factorial(num_bar))

def all_comb(N, factor_count_list):
    ans = 1
    for factor in factor_count_list:
        ans = (ans * comb(factor + N - 1, factor)) % (10 ** 9 + 7)
    return ans

def main():
    N, M = map(int, input().split())
    factor_count_list = Prime_Factorization(M)

    print(all_comb(N, factor_count_list))

if __name__ == "__main__":
    main()

Fixed code:
from math import *

def Prime_Factorization(M):
    factor_count_list = []
    root_M = int(sqrt(M))

    while root_M > 1:
        root_M = int(sqrt(M))

        for i in range(2, root_M + 1):
            e = 0
            while M % i == 0:
                e += 1
                M = M // i
            if e > 0:
                factor_count_list.append(e)
                break
        else:
            break

    if M > root_M:
        factor_count_list.append(1)

    return factor_count_list

def comb(num_object, num_bar):
    numerator = 1

    for i in range(num_bar):
        numerator = (numerator * (num_object - i))

    return  numerator // factorial(num_bar)

def all_comb(N, factor_count_list):
    ans = 1
    for factor in factor_count_list:
        ans = (ans * comb(factor + N - 1, factor)) % (10 ** 9 + 7)
    return ans

def main():
    N, M = map(int, input().split())
    factor_count_list = Prime_Factorization(M)

    print(all_comb(N, factor_count_list))

if __name__ == "__main__":
    main()
Buggy code:
import math

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

mod = 10**9 + 7
fac = [1, 1]
inv = [1, 1]
finv = [1, 1]
for i in range(2, n+5):
    fac.append(fac[i-1] * i % mod)
    inv.append(mod - inv[mod%i] * (mod//i) % mod)
    finv.append(finv[i-1] * inv[i] % mod)

def nck(n, k):
    if n < k:
        return 0
    if n < 0 or k < 0:
        return 0
    return fac[n] * (finv[k] * finv[n-k] % mod) % mod

sqrt_m = math.sqrt(m)
sqrt_m = int(sqrt_m) + 1
prime = []
for i in range(2, sqrt_m + 1):
    count = 0
    while m % i == 0:
        m = m // i
        count += 1
    if count > 0:
        prime.append(count)
if m > 1:
    prime.append(1)

ans = 1
for i in prime:
    ans *= nck(n-1+i, i)
    ans %= mod

print(ans)


Fixed code:
import math

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

sqrt_m = math.sqrt(m)
sqrt_m = int(sqrt_m) + 1

mod = 10**9 + 7
fac = [1, 1]
inv = [1, 1]
finv = [1, 1]
for i in range(2, n + 31):
    fac.append(fac[i-1] * i % mod)
    inv.append(mod - inv[mod%i] * (mod//i) % mod)
    finv.append(finv[i-1] * inv[i] % mod)

def nck(n, k):
    if n < k:
        return 0
    if n < 0 or k < 0:
        return 0
    return fac[n] * (finv[k] * finv[n-k] % mod) % mod


prime = []
for i in range(2, sqrt_m + 1):
    count = 0
    while m % i == 0:
        m = m // i
        count += 1
    if count > 0:
        prime.append(count)
if m > 1:
    prime.append(1)

ans = 1
for i in prime:
    ans *= nck(n-1+i, i)
    ans %= mod

print(ans)
Buggy code:
N,M=map(int,input().split())

def factorint(x):
  F={}
  i=2
  while i**2<=x:
    if x%i==0:
      c=0
      while x%i==0:
        x=x//i
        c+=1
      F[i]=c
    i+=1
  if x!=1:
    F[x]=1
  return F

def C(n,r):
  a=1
  b=1
  for i in range(r):
    a=a*(n-i)
    b=b*(r-i)
  return((a//b)%(10**9+7))

ans=1
print(factorint(M))
for f in factorint(M):
  k=factorint(M)[f]
  ans*=C(N+k-1,k)        
print(ans%((10**9)+7))


Fixed code:
N,M=map(int,input().split())

def factorint(x):
  F={}
  i=2
  while i**2<=x:
    if x%i==0:
      c=0
      while x%i==0:
        x=x//i
        c+=1
      F[i]=c
    i+=1
  if x!=1:
    F[x]=1
  return F

def C(n,r):
  a=1
  b=1
  for i in range(r):
    a=a*(n-i)
    b=b*(r-i)
  return((a//b)%(10**9+7))

ans=1
for f in factorint(M):
  k=factorint(M)[f]
  ans*=C(N+k-1,k)        
print(ans%((10**9)+7))
Buggy code:
def com(n,m):
    if(n-m < m):
        m=n-m
    result=1
    mylist=[i for i in range(1,m+1)]
    j=1
    for i in range(1,m+1):
        result*=(n+1-i)
        if(j<m):
            while(result%mylist[j]==0):
                result//=mylist[j]
                j+=1
                if(j>=m):
                    break
    return result

N,M=map(int,input().split())
soinsuubunkai={}
tmp=1
i=2
M
while(i*2 <=M):
    if(M%i==0):
        if(i in soinsuubunkai):
            soinsuubunkai[i]+=1
        else:
            soinsuubunkai[i]=1
        M//=i
    else:
        i+=1

tmp=1
for k in list(soinsuubunkai.values()):
    tmp*=com(k+N-1,k)
    tmp%=10**9+7
print(tmp)

Fixed code:
def com(n,m):
    if(n-m < m):
        m=n-m
    result=1
    mylist=[i for i in range(1,m+1)]
    j=1
    for i in range(1,m+1):
        result*=(n+1-i)
        if(j<m):
            while(result%mylist[j]==0):
                result//=mylist[j]
                j+=1
                if(j>=m):
                    break
    return result

def yakusuu(i,m):
    _i=i
    while(i**2<=m):
        if(m%i==0):
            return i
        else:
            i+=1
    for j in range(_i-1,0,-1):
        if(m%j==0):
            break
    return m//j
    

N,M=map(int,input().split())
soinsuubunkai={}
tmp=2
i=2
_M=M
while(tmp <=M):
    tmp=yakusuu(tmp,M)

    if(tmp in soinsuubunkai):
        soinsuubunkai[tmp]+=1
    else:
        soinsuubunkai[tmp]=1
    M//=tmp
    if(M==1):
        break


tmp=1
for k in list(soinsuubunkai.values()):
    tmp*=com(k+N-1,k)
    tmp%=10**9+7
print(tmp)
Buggy code:
N, M = map(int, input().split())
rec = []
MOD = 10 ** 9 + 7
K = M
for i in range(2, int(M ** 0.5) + 1):
    if K % i == 0:
        tmp = 0
        while K % i == 0:
            tmp += 1
            K //= i

        rec.append((i, tmp))

Q = 10 ** 6 + 1
fact = [0] * Q
rfact = [0] * Q
fact[0] = 1
for i in range(1, Q):
    fact[i] = fact[i - 1] * i % MOD

rfact[Q - 1] = pow(fact[Q - 1], MOD - 2, MOD)
for i in range(Q - 2, -1, -1):
    rfact[i] = rfact[i + 1] * (i + 1) % MOD


def comb(n, r):
    return fact[n] * rfact[n - r] * rfact[r] % MOD


num = 1
for i in range(len(rec)):
    num *= comb(N + rec[i][1] - 1, rec[i][1])
    num %= MOD

print(num)


Fixed code:
N, M = map(int, input().split())
rec = []
MOD = 10 ** 9 + 7
K = M
for i in range(2, int(M ** 0.5) + 1):
    if K % i == 0:
        tmp = 0
        while K % i == 0:
            tmp += 1
            K //= i

        rec.append((i, tmp))

if K != 1:
    rec.append((K, 1))
Q = 10 ** 6 + 1
fact = [0] * Q
rfact = [0] * Q
fact[0] = 1
for i in range(1, Q):
    fact[i] = fact[i - 1] * i % MOD

rfact[Q - 1] = pow(fact[Q - 1], MOD - 2, MOD)
for i in range(Q - 2, -1, -1):
    rfact[i] = rfact[i + 1] * (i + 1) % MOD


def comb(n, r):
    return fact[n] * rfact[n - r] * rfact[r] % MOD


num = 1
for i in range(len(rec)):
    num *= comb(N + rec[i][1] - 1, rec[i][1])
    num %= MOD

print(num)
Buggy code:
from collections import defaultdict
import math
N,M=map(int,input().split())
dd=defaultdict(int)
m=M
mod=10**9+7
for i in range(2,int(math.sqrt(M))+1):
    s=0
    while m%i==0 and m>1:
        m=m//i
        s+=1
    if s>0:
        dd[i]=s
def f(n,k):
    a=1
    for i in range(1,k+1):
        a=a*(n-i+1)
        a%=mod
        a*=pow(i,mod-2,mod)
        a%=mod
    return a
ans=1
for l,t in dd.items():
    ans*=f(N-1+t,t)
    ans%=mod
print(ans)



Fixed code:
from collections import defaultdict
import math
N,M=map(int,input().split())
dd=defaultdict(int)
m=M
mod=10**9+7
for i in range(2,10**5):
    s=0
    while m%i==0 and m>1:
        m=m//i
        s+=1
    if s>0:
        dd[i]=s
if m>1:
    dd[10**9]=1
def f(n,k):
    a=1
    for i in range(1,k+1):
        a=a*(n-i+1)
        a%=mod
        a*=pow(i,mod-2,mod)
        a%=mod
    return a
ans=1
for l,t in dd.items():
    ans*=f(N-1+t,t)
    ans%=mod
print(ans)
Buggy code:
import math


# """
def get_primes(n):
    primes = []
    checks = [True for _ in range(int(math.sqrt(n)))]
    checks[0] = checks[1] = False
    for i in range(2, len(checks)):
        if checks[i]:
            primes.append(i)
            tmp = 0
            while i + tmp * i < len(checks):
                checks[i + tmp * i] = False
                tmp += 1
    return primes


def combination(a, b):
    return math.factorial(a) // math.factorial(a - b) // math.factorial(b)


n, m = map(int, input().split())
primes = get_primes(m)
elems = []
m_copy = m
divides = dict()
for _p in primes:
    while m_copy % _p == 0:
        m_copy = m_copy // _p
        if str(_p) in divides.keys():
            divides[str(_p)] += 1
        else:
            divides[str(_p)] = 1
if m_copy > 1:
    divides[str(m_copy)] = 1
ans = 1
for i in divides.values():
    ans *= combination(i + n - 1, i)
print(ans % (1000000007))


Fixed code:
import math

# import time


def get_primes(n):
    primes = []
    checks = [True for _ in range(int(math.sqrt(n)) + 1)]
    checks[0] = checks[1] = False
    for i in range(2, len(checks)):
        if checks[i]:
            primes.append(i)
            tmp = 0
            while i + tmp * i < len(checks):
                checks[i + tmp * i] = False
                tmp += 1
    return primes


def combination(a, b):
    i = 1
    for _i in range(a - b + 1, a + 1):
        i *= _i
    return i // math.factorial(b)


n, m = map(int, input().split())
# start = time.time()
primes = get_primes(m)
elems = []
m_copy = m
divides = dict()
for _p in primes:
    while m_copy % _p == 0:
        m_copy = m_copy // _p
        if str(_p) in divides.keys():
            divides[str(_p)] += 1
        else:
            divides[str(_p)] = 1
if m_copy > 1:
    divides[str(m_copy)] = 1
# print(primes)

# print(time.time() - start)
ans = 1
for i in divides.values():
    ans *= combination(i + n - 1, i)
print(ans % (1000000007))
# print(time.time() - start)
Buggy code:
n,m=map(int,input().split())
i=2
s=[]
while i**2<m:
  j=0
  while m % (i**(j+1))==0:
    j+=1
  if j:
    m//=i**j
    s+=[j]
  i+=1
a=1
for v in s:
  c = 1
  for i in range(v):
    c = c * (n+i) // (1+i)
  a = a * c % (10**9+7)
print(a)


Fixed code:
n,m=map(int,input().split())
i=2
s=[]
while i*i<=m:
  j=0
  while m % i == 0:
    m//=i
    j+=1 
  if j:
    s+=[j]
  i+=1
a=1
if m > 1:
  s+=[1]
  
for v in s:
  c = 1
  for i in range(v):
    c = c * (n+i) // (1+i)
  a = a * c % (10**9+7)
print(a)
Buggy code:
n,m=map(int,input().split())
pw = []
d = 2
while d*d <= m:
  e = 0
  while m % d == 0:
    e += 1
    m //= d
  if e > 0: pw.append(e)
  d += 1
ans = 1
for e in pw:
  comb = 1
  for i in range(e):
    comb = comb * (n+i) // (1+i)
  ans = ans * comb % 1000000007
print(ans)

Fixed code:
n,m=map(int,input().split())
pw = []
d = 2
while d*d <= m:
  e = 0
  while m % d == 0:
    e += 1
    m //= d
  if e > 0: pw.append(e)
  d += 1
if m > 1: pw.append(1)
ans = 1
for e in pw:
  comb = 1
  for i in range(e):
    comb = comb * (n+i) // (1+i)
  ans = ans * comb % 1000000007
print(ans)
Buggy code:
import math
(n, m)  =map(int, input().split())
sqm = math.sqrt(m)
map = {}
i = 2
y = m
while m != 1 and sqm > i:
    if m % i == 0 :
        m = m / i
        if i in map:
            map[i] += 1
        else:
            map[i] = 1
    else:
        i += 1
sum = 1
for i in map:
    tmpn = n + map[i] - 1
    c = 1
    d = 1
    e = 1
    for j in range(map[i]):
        c = c * (tmpn - j)
        d = d * (map[i] - j)
    e = e * c // d
    
    sum = sum * e % 1000000007
print(sum )

Fixed code:
import math
(n, m)  =map(int, input().split())
sqm = math.sqrt(m)
map = {}
i = 2
y = m
while m != 1 and sqm >= i:
    if m % i == 0 :
        m = m / i
        if i in map:
            map[i] += 1
        else:
            map[i] = 1
    else:
        i += 1
if m > 1:
    map[m] = 1

sum = 1
for i in map:
    tmpn = n + map[i] - 1
    c = 1
    d = 1
    e = 1
    for j in range(map[i]):
        c = c * (tmpn - j)
        d = d * (map[i] - j)
    e = e * c // d
    
    sum = sum * e % 1000000007
print(sum )
Buggy code:
# -*- coding: utf-8 -*-
"""
Created on Sun Sep 23 22:00:37 2018
ABC110D
@author: maezawa
"""
import collections

def comb(n, r):
    if n == 0 or r == 0:
        return 1
    return comb(n, r-1)*(n-r+1)//r

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

mod = 10**9+7
np = int(10**4.5 + 10)
is_prime = [True]*(np+1)

is_prime[0] = False
is_prime[1] = False

for i in range(2, np//2):
    if is_prime[i] == True:
        for j in range(2*i,np+1,i):
            is_prime[j] = False

prime_numbers = [i for i in range(np+1) if is_prime[i]]

pds = []
for i in prime_numbers:
    if i > m:
        break
    if m%i == 0:
        pds.append(i)
        md = m//i
        while md%i == 0:
            #print(md)
            pds.append(i)
            md = md//i
        #pds.append(md)

print(pds)
cpds = collections.Counter(pds)
#print(cpds)
ans = 1
for i in cpds.values():
    ans = ans*comb(n+i-1,i)%mod

print(ans)


Fixed code:
# -*- coding: utf-8 -*-
"""
Created on Sun Sep 23 22:00:37 2018
ABC110D
@author: maezawa
"""
import collections

def comb(n, r):
    if n == 0 or r == 0:
        return 1
    return comb(n, r-1)*(n-r+1)//r

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

mod = 10**9+7
np = int(10**4.5 + 10)
is_prime = [True]*(np+1)

is_prime[0] = False
is_prime[1] = False

for i in range(2, np//2):
    if is_prime[i] == True:
        for j in range(2*i,np+1,i):
            is_prime[j] = False

prime_numbers = [i for i in range(np+1) if is_prime[i]]

pds = []
for i in prime_numbers:
    if i > m//2:
        break
    md = m
    while md%i == 0:
        pds.append(i)
        md = md//i
mul = 1
for i in pds:
    mul *= i
if m != mul:
    pds.append(m//mul)

#print(pds)
cpds = collections.Counter(pds)
#print(cpds)
ans = 1
for i in cpds.values():
    ans = ans*comb(n+i-1,i)%mod

print(ans)