Buggy python submission (verdict: Time Limit Exceeded):
mod = 10**9+7

def hurui(n):
  data = [i for i in range(2, n + 1)]
  for d in data:
    data = [x for x in data if (x == d or x % d != 0)]
  return data

MAX = 10**5 + 100

fac = [1]*(MAX+1)
for i in range(1,MAX+1):
    fac[i] = (fac[i-1]*i)%mod

rev_m = [1]*(MAX+1)
rev_m[MAX] = pow(fac[MAX],mod-2,mod)
for i in range(MAX,0,-1):
    rev_m[i-1] = (rev_m[i]*i)%mod

def Comb(n,k):#nCk
    return (fac[n]*rev_m[k]*rev_m[n-k])%mod


N,M = map(int, input().split())
Primes = hurui(4000)
kk = [0]*4000

while M > 1:
  for i,p in enumerate(Primes):
    if M%p == 0:
      kk[i]+=1
      M//=p
      break

ans =1
for k in kk:
  ans *= Comb(k+N-1,k)
  ans %= mod

print(ans)


Fixed submission:
from collections import defaultdict
import sys,heapq,bisect,math,itertools,string

def factors_nojit(n):
    gaps = [1,2,2,4,2,4,2,4,6,2,6]
    length, cycle = 11, 3
    f, fs, nxt = 2, [], 0
    while f * f <= n:
        while n % f == 0:
            fs.append(f)
            n0 = n
            n //= f
        f += gaps[nxt]
        nxt += 1
        if nxt == length:
            nxt = cycle
    if n > 1: fs.append(n)
    return fs

MAX = 10**5 + 100
mod = 10**9+7

fac = [1]*(MAX+1)
for i in range(1,MAX+1):
    fac[i] = (fac[i-1]*i)%mod

rev_m = [1]*(MAX+1)
rev_m[MAX] = pow(fac[MAX],mod-2,mod)
for i in range(MAX,0,-1):
    rev_m[i-1] = (rev_m[i]*i)%mod

def Comb(n,k):#nCk
    return (fac[n]*rev_m[k]*rev_m[n-k])%mod

N,M = map(int, input().split())

fs =  factors_nojit(M)
fs.sort()

dd = defaultdict(int)
ed = []
for f in fs:
    if dd[f] == 0:
        ed.append(f)
    dd[f] += 1

ans =1
for e in ed:
  k = dd[e]
  ans *= Comb(k+N-1,k)
  ans %= mod

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
mod = 10**9+7

def hurui(n):
  data = [i for i in range(2, n + 1)]
  for d in data:
    data = [x for x in data if (x == d or x % d != 0)]
  return data

MAX = 10**5 + 100

fac = [1]*(MAX+1)
for i in range(1,MAX+1):
    fac[i] = (fac[i-1]*i)%mod

rev_m = [1]*(MAX+1)
rev_m[MAX] = pow(fac[MAX],mod-2,mod)
for i in range(MAX,0,-1):
    rev_m[i-1] = (rev_m[i]*i)%mod

def Comb(n,k):#nCk
    return (fac[n]*rev_m[k]*rev_m[n-k])%mod


N,M = map(int, input().split())
Primes = hurui(4000)
kk = [0]*4000

while M > 1:
  for i,p in enumerate(Primes):
    if M%p == 0:
      kk[i]+=1
      M//=p
      break

ans =1
for k in kk:
  ans *= Comb(k+N-1,k)
  ans %= mod

print(ans)


Fixed submission:
from collections import defaultdict
import sys,heapq,bisect,math,itertools,string

def factors_nojit(n):
    gaps = [1,2,2,4,2,4,2,4,6,2,6]
    length, cycle = 11, 3
    f, fs, nxt = 2, [], 0
    while f * f <= n:
        while n % f == 0:
            fs.append(f)
            n0 = n
            n //= f
        f += gaps[nxt]
        nxt += 1
        if nxt == length:
            nxt = cycle
    if n > 1: fs.append(n)
    return fs

MAX = 10**5 + 100
mod = 10**9+7

fac = [1]*(MAX+1)
for i in range(1,MAX+1):
    fac[i] = (fac[i-1]*i)%mod

rev_m = [1]*(MAX+1)
rev_m[MAX] = pow(fac[MAX],mod-2,mod)
for i in range(MAX,0,-1):
    rev_m[i-1] = (rev_m[i]*i)%mod

def Comb(n,k):#nCk
    return (fac[n]*rev_m[k]*rev_m[n-k])%mod

N,M = map(int, input().split())

fs =  factors_nojit(M)
fs.sort()

dd = defaultdict(int)
ed = []
for f in fs:
    if dd[f] == 0:
        ed.append(f)
    dd[f] += 1

ans =1
for e in ed:
  k = dd[e]
  ans *= Comb(k+N-1,k)
  ans %= mod

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
mod = 10**9+7

def hurui(n):
  data = [i for i in range(2, n + 1)]
  for d in data:
    data = [x for x in data if (x == d or x % d != 0)]
  return data

MAX = 10**5 + 100

fac = [1]*(MAX+1)
for i in range(1,MAX+1):
    fac[i] = (fac[i-1]*i)%mod

rev_m = [1]*(MAX+1)
rev_m[MAX] = pow(fac[MAX],mod-2,mod)
for i in range(MAX,0,-1):
    rev_m[i-1] = (rev_m[i]*i)%mod

def Comb(n,k):#nCk
    return (fac[n]*rev_m[k]*rev_m[n-k])%mod


N,M = map(int, input().split())
Primes = hurui(8000)
kk = [0]*8000

while M > 1:
  for i,p in enumerate(Primes):
    if M%p == 0:
      kk[i]+=1
      M//=p
      break

ans =1
for k in kk:
  ans *= Comb(k+N-1,k)
  ans %= mod

print(ans)


Fixed submission:
from collections import defaultdict
import sys,heapq,bisect,math,itertools,string

def factors_nojit(n):
    gaps = [1,2,2,4,2,4,2,4,6,2,6]
    length, cycle = 11, 3
    f, fs, nxt = 2, [], 0
    while f * f <= n:
        while n % f == 0:
            fs.append(f)
            n0 = n
            n //= f
        f += gaps[nxt]
        nxt += 1
        if nxt == length:
            nxt = cycle
    if n > 1: fs.append(n)
    return fs

MAX = 10**5 + 100
mod = 10**9+7

fac = [1]*(MAX+1)
for i in range(1,MAX+1):
    fac[i] = (fac[i-1]*i)%mod

rev_m = [1]*(MAX+1)
rev_m[MAX] = pow(fac[MAX],mod-2,mod)
for i in range(MAX,0,-1):
    rev_m[i-1] = (rev_m[i]*i)%mod

def Comb(n,k):#nCk
    return (fac[n]*rev_m[k]*rev_m[n-k])%mod

N,M = map(int, input().split())

fs =  factors_nojit(M)
fs.sort()

dd = defaultdict(int)
ed = []
for f in fs:
    if dd[f] == 0:
        ed.append(f)
    dd[f] += 1

ans =1
for e in ed:
  k = dd[e]
  ans *= Comb(k+N-1,k)
  ans %= mod

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inp(): return int(input())
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

def hurui(n):
  data = [i for i in range(2, n + 1)]
  for d in data:
    data = [x for x in data if (x == d or x % d != 0)]
  return data

MAX = 2*(10**5)

fac = [1]*(MAX+1)
for i in range(1,MAX+1):
    fac[i] = (fac[i-1]*i)%mod

rev_m = [1]*(MAX+1)
rev_m[MAX] = pow(fac[MAX],mod-2,mod)
for i in range(MAX,0,-1):
    rev_m[i-1] = (rev_m[i]*i)%mod

def Comb(n,k):#nCk
    return (fac[n]*rev_m[k]*rev_m[n-k])%mod


N,M = inpl()
Primes = hurui(10000)
kk = [0]*10000

while M > 1:
  for i,p in enumerate(Primes):
    if M%p == 0:
      kk[i]+=1
      M//=p
      break
      
ans =1
for k in kk:
  ans *= Comb(k+N-1,k)
  ans %= mod
  
print(ans)
  






Fixed submission:
from collections import defaultdict
import sys,heapq,bisect,math,itertools,string

def factors_nojit(n):
    gaps = [1,2,2,4,2,4,2,4,6,2,6]
    length, cycle = 11, 3
    f, fs, nxt = 2, [], 0
    while f * f <= n:
        while n % f == 0:
            fs.append(f)
            n0 = n
            n //= f
        f += gaps[nxt]
        nxt += 1
        if nxt == length:
            nxt = cycle
    if n > 1: fs.append(n)
    return fs

MAX = 10**5 + 100
mod = 10**9+7

fac = [1]*(MAX+1)
for i in range(1,MAX+1):
    fac[i] = (fac[i-1]*i)%mod

rev_m = [1]*(MAX+1)
rev_m[MAX] = pow(fac[MAX],mod-2,mod)
for i in range(MAX,0,-1):
    rev_m[i-1] = (rev_m[i]*i)%mod

def Comb(n,k):#nCk
    return (fac[n]*rev_m[k]*rev_m[n-k])%mod

N,M = map(int, input().split())

fs =  factors_nojit(M)
fs.sort()

dd = defaultdict(int)
ed = []
for f in fs:
    if dd[f] == 0:
        ed.append(f)
    dd[f] += 1

ans =1
for e in ed:
  k = dd[e]
  ans *= Comb(k+N-1,k)
  ans %= mod

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict,deque
import sys,heapq,bisect,math,itertools,string,queue,datetime
sys.setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inp(): return int(input())
def inpl(): return list(map(int, input().split()))
def inpls(): return list(input().split())

def hurui(n):
  data = [i for i in range(2, n + 1)]
  for d in data:
    data = [x for x in data if (x == d or x % d != 0)]
  return data

MAX = 3*(10**5)

fac = [1]*(MAX+1)
for i in range(1,MAX+1):
    fac[i] = (fac[i-1]*i)%mod

rev_m = [1]*(MAX+1)
rev_m[MAX] = pow(fac[MAX],mod-2,mod)
for i in range(MAX,0,-1):
    rev_m[i-1] = (rev_m[i]*i)%mod

def Comb(n,k):#nCk
    return (fac[n]*rev_m[k]*rev_m[n-k])%mod


N,M = inpl()
Primes = hurui(10000)
kk = [0]*10000

while M > 1:
  for i,p in enumerate(Primes):
    if M%p == 0:
      kk[i]+=1
      M//=p
      break
      
ans =1
for k in kk:
  ans *= Comb(k+N-1,k)
  ans %= mod
  
print(ans)
  






Fixed submission:
from collections import defaultdict
import sys,heapq,bisect,math,itertools,string

def factors_nojit(n):
    gaps = [1,2,2,4,2,4,2,4,6,2,6]
    length, cycle = 11, 3
    f, fs, nxt = 2, [], 0
    while f * f <= n:
        while n % f == 0:
            fs.append(f)
            n0 = n
            n //= f
        f += gaps[nxt]
        nxt += 1
        if nxt == length:
            nxt = cycle
    if n > 1: fs.append(n)
    return fs

MAX = 10**5 + 100
mod = 10**9+7

fac = [1]*(MAX+1)
for i in range(1,MAX+1):
    fac[i] = (fac[i-1]*i)%mod

rev_m = [1]*(MAX+1)
rev_m[MAX] = pow(fac[MAX],mod-2,mod)
for i in range(MAX,0,-1):
    rev_m[i-1] = (rev_m[i]*i)%mod

def Comb(n,k):#nCk
    return (fac[n]*rev_m[k]*rev_m[n-k])%mod

N,M = map(int, input().split())

fs =  factors_nojit(M)
fs.sort()

dd = defaultdict(int)
ed = []
for f in fs:
    if dd[f] == 0:
        ed.append(f)
    dd[f] += 1

ans =1
for e in ed:
  k = dd[e]
  ans *= Comb(k+N-1,k)
  ans %= mod

print(ans)