Buggy python submission (verdict: Time Limit Exceeded):
N, M = [ int(it) for it in input().split() ]
MOD = 1000000007

import math
sM = int(math.sqrt(M)+1)

p_li = []
m = M
for i in range(sM):
  for j in range(2,sM+1):
    if (m%j)==0:
      p_li.append(j)
      m//=j
      break
  if (m==1):
    break
if (m!=1):
  p_li.append(m)
    
    
import collections
co = collections.Counter(p_li)
vec = co.values()

def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    #[x,y]
    return [w[0],w[1]]

# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m

s = 1
for v in vec:
  X=N-1+v
  Y=N-1
  if (X-Y<Y):
    Y=X-Y
  ss = 1
  sd = 1
  for i in range(X,X-Y,-1):
    ss = (ss*i)%MOD
  for i in range(Y,0,-1):
    sd = (sd*i)%MOD
  
  ss = (ss*mod_inv(sd,MOD))%MOD
  s = (s*ss)%MOD
print (s%MOD)
      




Fixed submission:
N, M = [ int(it) for it in input().split() ]
MOD = 1000000007

import math
sM = int(math.sqrt(M)+1)

p_li = []
m = M
for j in range(2,sM+1):
  for i in range(sM):
    if (m%j)==0:
      p_li.append(j)
      m//=j
    else:
      break
  if (m==1):
    break
if (m!=1):
  p_li.append(m)
    
    
import collections
co = collections.Counter(p_li)
vec = co.values()

def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    #[x,y]
    return [w[0],w[1]]

# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m

s = 1
for v in vec:
  X=N-1+v
  Y=N-1
  if (X-Y<Y):
    Y=X-Y
  ss = 1
  sd = 1
  for i in range(X,X-Y,-1):
    ss = (ss*i)%MOD
  for i in range(Y,0,-1):
    sd = (sd*i)%MOD
  
  ss = (ss*mod_inv(sd,MOD))%MOD
  s = (s*ss)%MOD
print (s%MOD)

Buggy python submission (verdict: Time Limit Exceeded):
N, M = [ int(it) for it in input().split() ]
MOD = 1000000007

import math
sM = int(math.sqrt(M)+1)

p_li = []
m = M
for i in range(sM):
  for j in range(2,sM+1):
    if (m%j)==0:
      p_li.append(j)
      m//=j
      break
  if (m==1):
    break
if (m!=1):
  p_li.append(m)
    
    
import collections
co = collections.Counter(p_li)
vec = co.values()

def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    #[x,y]
    return [w[0],w[1]]

# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m

s = 1
for v in vec:
  X=N-1+v
  Y=N-1
  if (X-Y<Y):
    Y=X-Y
  ss = 1
  for i in range(X,X-Y,-1):
    ss = (ss*i)%MOD
  for i in range(Y,0,-1):
    ss = (ss*mod_inv(i,MOD))%MOD
  s = (s*ss)%MOD
print (s%MOD)
      




Fixed submission:
N, M = [ int(it) for it in input().split() ]
MOD = 1000000007

import math
sM = int(math.sqrt(M)+1)

p_li = []
m = M
for j in range(2,sM+1):
  for i in range(sM):
    if (m%j)==0:
      p_li.append(j)
      m//=j
    else:
      break
  if (m==1):
    break
if (m!=1):
  p_li.append(m)
    
    
import collections
co = collections.Counter(p_li)
vec = co.values()

def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    #[x,y]
    return [w[0],w[1]]

# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m

s = 1
for v in vec:
  X=N-1+v
  Y=N-1
  if (X-Y<Y):
    Y=X-Y
  ss = 1
  sd = 1
  for i in range(X,X-Y,-1):
    ss = (ss*i)%MOD
  for i in range(Y,0,-1):
    sd = (sd*i)%MOD
  
  ss = (ss*mod_inv(sd,MOD))%MOD
  s = (s*ss)%MOD
print (s%MOD)

Buggy python submission (verdict: Time Limit Exceeded):
N, M = [ int(it) for it in input().split() ]
MOD = 1000000007

import math
sM = int(math.sqrt(M)+1)

p_li = []
m = M
for i in range(sM):
  for j in range(2,sM+1):
    if (m%j)==0:
      p_li.append(j)
      m//=j
      break
  if (m==1):
    break
if (m!=1):
  p_li.append(m)
    
    
import collections
co = collections.Counter(p_li)
vec = co.values()

def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    #[x,y]
    return [w[0],w[1]]

# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m
  
s = 1
for v in vec:
  
  ss = 1
  for i in range(N-1+v,v,-1):
    ss = (ss*i)%MOD
  for i in range(N-1,0,-1):
    ss = (ss*mod_inv(i,MOD))%MOD
  s *= (ss%MOD)
  s = s%MOD
print (s%MOD)
      




Fixed submission:
N, M = [ int(it) for it in input().split() ]
MOD = 1000000007

import math
sM = int(math.sqrt(M)+1)

p_li = []
m = M
for j in range(2,sM+1):
  for i in range(sM):
    if (m%j)==0:
      p_li.append(j)
      m//=j
    else:
      break
  if (m==1):
    break
if (m!=1):
  p_li.append(m)
    
    
import collections
co = collections.Counter(p_li)
vec = co.values()

def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    #[x,y]
    return [w[0],w[1]]

# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m

s = 1
for v in vec:
  X=N-1+v
  Y=N-1
  if (X-Y<Y):
    Y=X-Y
  ss = 1
  sd = 1
  for i in range(X,X-Y,-1):
    ss = (ss*i)%MOD
  for i in range(Y,0,-1):
    sd = (sd*i)%MOD
  
  ss = (ss*mod_inv(sd,MOD))%MOD
  s = (s*ss)%MOD
print (s%MOD)