Problem:


Score : 400 points

Problem Statement

You are given positive integers N and M.

How many sequences a of length N consisting of positive integers satisfy a_1 \times a_2 \times ... \times a_N = M? Find the count modulo 10^9+7.

Here, two sequences a' and a'' are considered different when there exists some i such that a_i' \neq a_i''.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of the sequences consisting of positive integers that satisfy the condition, modulo 10^9 + 7.

Sample Input 1

2 6

Sample Output 1

4

Four sequences satisfy the condition: \{a_1, a_2\} = \{1, 6\}, \{2, 3\}, \{3, 2\} and \{6, 1\}.

Sample Input 2

3 12

Sample Output 2

18

Sample Input 3

100000 1000000000

Sample Output 3

957870001



Sample input:
2 6


Sample output:
4

Submission status: Wrong Answer

Solution code:
n, m = map(int, input().split())
mod = 10**9+7
modp = mod
max_n = 10 ** 6 + 1               # 必要分だけ用意する
fact = [1, 1] + [0]*max_n     # fact[n] = (n! mod modp)
factinv = [1, 1] + [0]*max_n  # factinv[n] = ((n!)^(-1) mod modp)
inv = [0, 1] + [0]*max_n      # factinv 計算用

def cmb(n, r, p):
    assert n < p, 'n is less than modp'
    assert n < max_n, 'n in less than max_n'
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p

for i in range(2, max_n + 1):
    fact[i] = (fact[i-1] * i) % modp
    inv[i] = (-inv[modp % i] * (modp // i)) % modp
    factinv[i] = (factinv[i-1] * inv[i]) % modp

def factorization(m):
    arr = []
    temp = m
    # 一旦負にするとceilと同じ挙動となる。//1はfloatを返すのでintが必要
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt = 0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])
    
    if temp!=1:
        arr.append([temp, 1])
    
    if arr==[]:
        arr.append([n, 1])
    return arr

arr = factorization(m)

ans = 1
for k, v in arr:
    temp = cmb(v+n-1, v, mod)
    ans = (ans * temp) % mod
print(ans)

Submission status: Wrong Answer

Solution code:
import sys
import itertools
# import numpy as np
import time
import math
import heapq
from collections import defaultdict
sys.setrecursionlimit(10 ** 7)
 
INF = 10 ** 18
MOD = 10 ** 9 + 7
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

# map(int, input().split())

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

fact = []

X = M
i = 2
while i ** 2 <= X:
    v = 0
    while M % i == 0:
        M //= i
        v += 1
    if v != 0:
        fact.append(v)
    i += 1
if M != 1:
    fact.append(v)

MAX = 2 * 10 ** 5
MOD = 10 ** 9 + 7

fac = [0 for i in range(MAX)]
finv = [0 for i in range(MAX)]
inv = [0 for i in range(MAX)]

def comInit(mod):
    fac[0], fac[1] = 1, 1
    finv[0], finv[1] = 1, 1
    inv[1] = 1
    for i in range(2, MAX):
        fac[i] = fac[i - 1] * i % mod
        inv[i] = mod - inv[mod % i] * (mod // i) % mod
        finv[i] = finv[i - 1] * inv[i] % mod


def com(n, r, mod):
    if n < r:
        return 0
    if n < 0 or r < 0:
        return 0
    return fac[n] * (finv[r] * finv[n - r] % mod) % mod
    
comInit(MOD)


ans = 1
for f in fact:
    ans *= com(f + N - 1, N - 1, MOD)
    ans %= MOD
print(ans)

Submission status: Wrong Answer

Solution code:
# -*- coding: utf-8 -*-

#############
# Libraries #
#############

import sys
input = sys.stdin.readline

import math
#from math import gcd
import bisect
import heapq
from collections import defaultdict
from collections import deque
from collections import Counter
from functools import lru_cache

#############
# Constants #
#############

MOD = 10**9+7
INF = float('inf')
AZ = "abcdefghijklmnopqrstuvwxyz"

#############
# Functions #
#############

######INPUT######
def I(): return int(input().strip())
def S(): return input().strip()
def IL(): return list(map(int,input().split()))
def SL(): return list(map(str,input().split()))
def ILs(n): return list(int(input()) for _ in range(n))
def SLs(n): return list(input().strip() for _ in range(n))
def ILL(n): return [list(map(int, input().split())) for _ in range(n)]
def SLL(n): return [list(map(str, input().split())) for _ in range(n)]

######OUTPUT######
def P(arg): print(arg); return
def Y(): print("Yes"); return
def N(): print("No"); return
def E(): exit()
def PE(arg): print(arg); exit()
def YE(): print("Yes"); exit()
def NE(): print("No"); exit()

#####Shorten#####
def DD(arg): return defaultdict(arg)

#####Inverse#####
def inv(n): return pow(n, MOD-2, MOD)

######Combination######
kaijo_memo = []
def kaijo(n):
  if(len(kaijo_memo) > n): return kaijo_memo[n]
  if(len(kaijo_memo) == 0): kaijo_memo.append(1)
  while(len(kaijo_memo) <= n): kaijo_memo.append(kaijo_memo[-1] * len(kaijo_memo) % MOD)
  return kaijo_memo[n]

gyaku_kaijo_memo = []
def gyaku_kaijo(n):
  if(len(gyaku_kaijo_memo) > n): return gyaku_kaijo_memo[n]
  if(len(gyaku_kaijo_memo) == 0): gyaku_kaijo_memo.append(1)
  while(len(gyaku_kaijo_memo) <= n): gyaku_kaijo_memo.append(gyaku_kaijo_memo[-1] * pow(len(gyaku_kaijo_memo),MOD-2,MOD) % MOD)
  return gyaku_kaijo_memo[n]

def nCr(n,r):
  if n == r: return 1
  if n < r or r < 0: return 0
  ret = 1
  ret = ret * kaijo(n) % MOD
  ret = ret * gyaku_kaijo(r) % MOD
  ret = ret * gyaku_kaijo(n-r) % MOD
  return ret

######Factorization######
def factorization(n):
  arr = []
  temp = n
  for i in range(2, int(-(-n**0.5//1))+1):
    if temp%i==0:
      cnt=0
      while temp%i==0: 
        cnt+=1 
        temp //= i
      arr.append([i, cnt])
  if temp!=1: arr.append([temp, 1])
  if arr==[]: arr.append([n, 1])
  return arr

#####MakeDivisors######
def make_divisors(n):
  divisors = []
  for i in range(1, int(n**0.5)+1):
    if n % i == 0:
      divisors.append(i)
      if i != n // i: 
        divisors.append(n//i)
  return divisors

#####MakePrimes######
def make_primes(N):
  max = int(math.sqrt(N))
  seachList = [i for i in range(2,N+1)]
  primeNum = []
  while seachList[0] <= max:
    primeNum.append(seachList[0])
    tmp = seachList[0]
    seachList = [i for i in seachList if i % tmp != 0]
  primeNum.extend(seachList)
  return primeNum

#####GCD#####
def gcd(a, b):
    while b: a, b = b, a % b
    return a

#####LCM#####
def lcm(a, b):
    return a * b // gcd (a, b)

#####BitCount#####
def count_bit(n):
  count = 0
  while n:
    n &= n-1
    count += 1
  return count

#####ChangeBase#####
def base_10_to_n(X, n):
  if X//n: return base_10_to_n(X//n, n)+[X%n]
  return [X%n]

def base_n_to_10(X, n):
  return sum(int(str(X)[-i-1])*n**i for i in range(len(str(X))))

def base_10_to_n_without_0(X, n):
  X -= 1
  if X//n: return base_10_to_n_without_0(X//n, n)+[X%n]
  return [X%n]

#####IntLog#####
def int_log(n, a):
  count = 0
  while n>=a:
    n //= a
    count += 1
  return count

#############
# Main Code #
#############

N,M = IL()
ans = 1
for p,n in factorization(M):
  if p==1:
    pass
    exit()
  else:
    ans *= nCr(n+N-1,N-1)
    ans %= MOD
print(ans)

Submission status: Wrong Answer

Solution code:
n,m=map(int,input().split())

def prime_factorize(n):
    n_origin=n+0
    primelist=[]
    a=2
    while a*a<=n_origin:
        if n%a!=0:
            a+=1
            continue
        ex=0
        while n%a==0:
            ex+=1
            n=n//a
        primelist.append([a,ex])
        a+=1
    if n!=1:
        primelist.append([n,1])
    return primelist

#nCkをmodで割ったあまり
#テーブルを作る前処理
mod=10**9+7
fac=[0,1]
finv=[0,1]
inv=[0,1]
nmax=110000
for i in range(2,nmax+1):
    fac.append(fac[i-1]*i%mod)
    inv.append(mod-inv[mod%i]*(mod//i)%mod)
    finv.append(finv[i-1]*inv[i]%mod)
#二項係数計算部分
def combinations_mod(n,k,mod):
    if n<k:
        return 0
    if n<0 or k<0 :
        return 0
    return fac[n]*(finv[k]*finv[n-k]%mod)%mod
primelist=prime_factorize(m)
ans=1
for pi,bi in primelist:
    ans=(ans*combinations_mod(bi+n-1,n-1,mod))%mod
print(ans)

Submission status: Wrong Answer

Solution code:
n,m=map(int,input().split())

def prime_factorize(n):
    n_origin=n+0
    primelist=[]
    a=2
    while a*a<=n_origin:
        if n%a!=0:
            a+=1
            continue
        ex=0
        while n%a==0:
            ex+=1
            n=n//a
        primelist.append([a,ex])
        a+=1
    if n!=1:
        primelist.append([n,1])
    return primelist

#nCkをmodで割ったあまり
#テーブルを作る前処理
mod=10**9+7
fac=[0,1]
finv=[0,1]
inv=[0,1]
nmax=110000
for i in range(2,nmax+1):
    fac.append(fac[i-1]*i%mod)
    inv.append(mod-inv[mod%i]*(mod//i)%mod)
    finv.append(finv[i-1]*inv[i]%mod)
#二項係数計算部分
def combinations_mod(n,k,mod):
    if n<k:
        return 0
    if n<0 or k<0 :
        return 0
    return fac[n]*(finv[k]*finv[n-k]%mod)%mod
primelist=prime_factorize(m)
ans=1
for pi,bi in primelist:
    ans=(ans*combinations_mod(bi+n-1,bi,mod))%mod
print(ans)

Submission status: Wrong Answer

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


def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append([i, cnt])
    if temp != 1:
        arr.append([temp, 1])

    if arr == [] and n != 1:
        arr.append([n, 1])

    return arr


mod = 10**9 + 7


def cmb(n, r, mod):
    if (r < 0 or r > n):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod


g1 = [1, 1]  # 元テーブル
g2 = [1, 1]  # 逆元テーブル
inverse = [0, 1]  # 逆元テーブル計算用テーブル

for i in range(2, N + 1):
    g1.append((g1[-1] * i) % mod)
    inverse.append((-inverse[mod % i] * (mod//i)) % mod)
    g2.append((g2[-1] * inverse[-1]) % mod)


primes = factorization(M)
# 何箇所に分けるか（cnt以下）,その中でどう分けるか（しきりをどこにおくか（振り分けられないものが出ると選べれないのとおなじになるので、cnt - 選んだ数））
print(primes)
if N == 1:
    print(1)
    exit(0)
ans = 1

for p, cnt in primes:
    tmp = 0
    for i in range(1, min(cnt, N)+1):
        tmp += cmb(N, i, mod) * cmb(cnt-1, i-1, mod)
        #print(tmp, p, cnt, i)
        tmp %= mod
    ans *= tmp
    ans %= mod

print(ans)

Submission status: Wrong Answer

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


def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append([i, cnt])
    if temp != 1:
        arr.append([temp, 1])

    if arr == []:
        arr.append([n, 1])

    return arr


mod = 10**9 + 7


def cmb(n, r, mod):
    if (r < 0 or r > n):
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod


g1 = [1, 1]  # 元テーブル
g2 = [1, 1]  # 逆元テーブル
inverse = [0, 1]  # 逆元テーブル計算用テーブル

for i in range(2, N + 1):
    g1.append((g1[-1] * i) % mod)
    inverse.append((-inverse[mod % i] * (mod//i)) % mod)
    g2.append((g2[-1] * inverse[-1]) % mod)


primes = factorization(M)
# 何箇所に分けるか（cnt以下）,その中でどう分けるか（しきりをどこにおくか（振り分けられないものが出ると選べれないのとおなじになるので、cnt - 選んだ数））

if N == 1:
    print(1)
    exit(0)
ans = 1
for p, cnt in primes:
    tmp = 0
    for i in range(1, min(cnt, N)+1):
        tmp += cmb(N, i, mod) * cmb(cnt-1, i-1, mod)
        #print(tmp, p, cnt, i)
        tmp %= mod
    ans *= tmp
    ans %= mod

print(ans)

Submission status: Wrong Answer

Solution code:
from sys import stdin
input = stdin.readline


class PrimeComb:
  def __init__(self, MAX=510000, MOD=1000000007):
    self.MAX  = MAX
    self.MOD  = MOD
    self.fac  = [0]*MAX
    self.inv  = [0]*MAX
    self.finv = [0]*MAX
    self.fac[0] = self.fac[1] = 1
    self.inv[0] = self.inv[1] = 1
    self.finv[1] = 1
    for i in range(2, MAX):
      self.fac[i]  = self.fac[i-1] * i % MOD
      self.inv[i]  = MOD - self.inv[MOD % i] * int(MOD / i) % MOD
      self.finv[i] = self.finv[i-1] * self.inv[i] % MOD

  def com(self, n, k):
    # compute -> nCk % self.P
    if (n < k): return 0
    if (n < k or k < 0): return 0
    return self.fac[n] * (self.finv[k] * self.finv[n-k] % self.MOD) % self.MOD


def prime_fatorization(n):
  from collections import defaultdict
  # a = []
  a = defaultdict(int)
  while not(n % 2):
    # a.append(2)
    a[2] += 1
    n //= 2
  f = 3
  while f * f <= n:
    if not(n % f):
      # a.append(f)
      a[f] += 1
      n //= f
    else:
      f += 2
  if n != 1:
    # a.append(n)
    a[n] += 1
  return a


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

  PC = PrimeComb(200000)
  P = prime_fatorization(M)
  ans = 1
  for k in P.values():
    ans *= PC.com(N-1+k, k)
    # print(N-1+k, 'C', k, PC.com(N-1+k, k))
  # print(P)
  print(ans % 1000000007)


if(__name__ == '__main__'):
  main()

Submission status: Wrong Answer

Solution code:
from sys import stdin
input = stdin.readline


class PrimeComb:
  def __init__(self, MAX=510000, MOD=1000000007):
    self.MAX  = MAX
    self.MOD  = MOD
    self.fac  = [0]*MAX
    self.inv  = [0]*MAX
    self.finv = [0]*MAX
    self.fac[0] = self.fac[1] = 1
    self.inv[0] = self.inv[1] = 1
    self.finv[1] = 1
    for i in range(2, MAX):
      self.fac[i]  = self.fac[i-1] * i % MOD
      self.inv[i]  = MOD - self.inv[MOD % i] * int(MOD / i) % MOD
      self.finv[i] = self.finv[i-1] * self.inv[i] % MOD

  def com(self, n, k):
    # compute -> nCk % self.P
    if (n < k): return 0
    if (n < k or k < 0): return 0
    return self.fac[n] * (self.finv[k] * self.finv[n-k] % self.MOD) % self.MOD


def prime_fatorization(n):
  from collections import defaultdict
  # a = []
  a = defaultdict(int)
  while not(n % 2):
    # a.append(2)
    a[2] += 1
    n //= 2
  f = 3
  while f * f <= n:
    if not(n % f):
      # a.append(f)
      a[f] += 1
      n //= f
    else:
      f += 2
  if n != 1:
    # a.append(n)
    a[n] += 1
  return a


def main():
  N, M = list(map(int, input().split()))
  print(N)
  print(M)

  PC = PrimeComb(200000)
  P = prime_fatorization(M)
  ans = 1
  for k in P.values():
    ans *= PC.com(N-1+k, k)
    # print(N-1+k, 'C', k, PC.com(N-1+k, k))
  # print(P)
  print(ans % 1000000007)


if(__name__ == '__main__'):
  main()

Submission status: Wrong Answer

Solution code:
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from collections import defaultdict, deque, Counter
from sys import exit
from decimal import *
import heapq
import math
from fractions import gcd
import random
import string
import copy
from itertools import combinations, permutations, product
from operator import mul
from functools import reduce
from bisect import bisect_left, bisect_right

import sys
sys.setrecursionlimit(1000000000)
mod = 10 ** 9 + 7


#############
# Main Code #
#############

N, M = getNM()

def cmb_2(x,y):
    r = 1
    for i in range(1, y + 1):
        r = (r * (x - i + 1) * pow(i, mod - 2, mod)) % mod
    return r

def prime_factorize(n):
    divisors = []
    # 27(2 * 2 * 7)の7を出すためにtemp使う
    temp = n
    for i in range(2, int(math.sqrt(n)) + 1):
        if temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                # 素因数を見つけるたびにtempを割っていく
                temp //= i
            divisors.append([i, cnt])
    if temp != 1:
        divisors.append([temp, 1])
    if divisors == []:
        divisors.append([n, 1])

    return divisors

num = prime_factorize(M)

ans = 1
for i in num:
    ans *= cmb_2(N + i[1] - 1, i[1])
    ans %= mod
print(ans)

Submission status: Wrong Answer

Solution code:
from collections import Counter

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

MOD = 10 ** 9 + 7

# 素因数分解
power = []
p = 2
mm = m # m をあとで使うので
while mm > 1:
    if mm % p == 0:
        while True:
            if mm % p != 0:
                break
            power.append(p)
            mm //= p
    p += 1

# コンビネーション計算用
fact = [0] * 1100000
invfact = [0] * 1100000

fact[0] = 1
for i in range(1, 1100000):
    fact[i] = fact[i - 1] * i % MOD

# fermat
invfact[1100000 - 1] = pow(fact[1100000 - 1], MOD - 2, MOD)

for i in range(1100000 - 1, 0, -1):
    invfact[i - 1] = invfact[i] * i % MOD

def comb(n, k):
    return fact[n] * invfact[k] * invfact[n - k] % MOD

if m == 1:
    print(1)
else:
    res = 1
    c = Counter(power)
    print(c)
    for k, v in c.items():
        res *= comb(v + n - 1, n - 1)
        res %= MOD
    print(res)

Submission status: Wrong Answer

Solution code:
N,M=map(int,input().split())
mod=10**9+7

def nCmMOD(A,B,Mod):
    #a conb b を　Mod で割った余り
    num,den=1,1
    for i in range(B):
        num*=(A-i)
        den*=(i+1)
        num%=Mod
        den%=Mod
    return (num*pow(den,Mod-2,Mod))%Mod

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])
    if temp!=1:
        arr.append([temp, 1])
    if arr==[]:
        arr.append([n, 1])
    return arr

ans=1
F=factorization(M)
#print(F)
for i in range(len(F)):
    f=F[i][1]
    ans*=nCmMOD(f+N-1,f,mod)
    ans%=mod

print(ans)

Submission status: Wrong Answer

Solution code:
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


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

def factor(n, m=None):
    # mを与えると、高々その素因数まで見て、残りは分解せずにそのまま出力する
    arr = {}
    temp = n
    M = int(-(-n**0.5//1))+1
    if m is not None:
        M = min(m+1, M)
    for i in range(2, M):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr[i] = cnt

    if temp!=1:
        arr[temp] = 1

    if not arr:
        arr[n] = 1

    return arr
  
d = factor(m)
M = 10**9+7 # 出力の制限
N = max(d.values())+10+n # 必要なテーブルサイズ

g1 = [None] * (N+1) # 元テーブル
g2 = [None] * (N+1) #逆元テーブル
inverse = [None] * (N+1) #逆元テーブル計算用テーブル
g1[0] = g1[1] = g2[0] = g2[1] = 1
inverse[0], inverse[1] = [0, 1] 

for i in range( 2, N + 1 ):
    g1[i] = ( g1[i-1] * i ) % M 
    inverse[i] = ( -inverse[M % i] * (M//i) ) % M # ai+b==0 mod M <=> i==-b*a^(-1) <=> i^(-1)==-b^(-1)*aより
    g2[i] = (g2[i-1] * inverse[i]) % M 

def cmb(n, r, M):
    if ( r<0 or r>n ):
        return 0
    r = min(r, n-r)
    return (g1[n] * g2[r] * g2[n-r]) % M

ans = 1
for v in d.values():
    ans *= cmb(v+n-1, n-1, M)
    ans %= M
print(ans)

Submission status: Wrong Answer

Solution code:
n,m=map(int,input().split())
mod=pow(10,9)+7
def factorization(n):
  arr = []
  temp = n
  for i in range(2, int(-(-n**0.5//1))+1):
    if temp%i==0:
      cnt=0
      while temp%i==0:
        cnt+=1
        temp //= i
      arr.append([i, cnt])
  if temp!=1:
    arr.append([temp, 1])
  if arr==[]:
    arr.append([n, 1])
  return arr

# コンビネーション、さらに高速。あらかじめO(N)の計算をすることでのちの計算が早くなる
def cmb(n,r,mod):
  if (r<0 or r>n):
    return 0
  r=min(r,n-r)
  return g1[n]*g2[r]*g2[n-r]%mod
g1=[1,1] 
g2=[1,1] 
inverse=[0,1]
for i in range(2,n+30+1):
  g1.append((g1[-1]*i)%mod)
  inverse.append((-inverse[mod%i]*(mod//i))%mod)
  g2.append((g2[-1]*inverse[-1])%mod)

l=factorization(m)
ans=1
for li in l:
  b=li[1]
  ans*=cmb(b+n-1,n-1,mod)
  ans%=mod
print(ans)

Submission status: Wrong Answer

Solution code:
def main():
    from operator import mul
    from functools import reduce
    def cmb(n, r):
        r = min(n - r, r)
        if r == 0: return 1
        over = reduce(mul, range(n, n - r, -1))
        under = reduce(mul, range(1, r + 1))
        return over // under
    def factorization(n):
        arr = []
        temp = n
        for i in range(2, int(-(-n ** 0.5 // 1)) + 1):
            if temp % i == 0:
                cnt = 0
                while temp % i == 0:
                    cnt += 1
                    temp //= i
                arr.append([i, cnt])
        if temp != 1:
            arr.append([temp, 1])
        if arr == []:
            arr.append([n, 1])
        return arr

    large_p = 10 ** 9 + 7
    n, m = map(int, input().split())
    mp = factorization(m)
    mp2 = sum([f[1] for f in mp])
    r = 1
    for mpe in mp:
        #tmp = cmb(mpe[1] + n - 1, mpe[1])
        tmp = cmb(mpe[1] + n - 1, n - 1)
        r = r * tmp
        r = r % large_p
    if r < 0:
        r += large_p
    print(r)

if __name__ == '__main__':
    main()

Submission status: Wrong Answer

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

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(n**0.5//1+1)):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    # if arr==[]:
    #     arr.append([n, 1])

    return arr

arr = factorization(m)
if not arr:
    print(1)
    exit()
ans = 1
for a, b in arr:
    pattern = factorial(b+n-1) // (factorial(b) * factorial(n-1))
    print(b+n-1)
    print(n-1)
    ans = (ans * pattern)%mod

print(ans)

Submission status: Wrong Answer

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

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(n**0.5//1+1)):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

arr = factorization(m)
ans = 1
for a, b in arr:
    pattern = factorial(b+n-1) // (factorial(b) * factorial(n-1))
    ans = (ans * pattern)%mod

print(ans)

Submission status: Wrong Answer

Solution code:
n,m=map(int,input().split())

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

score=factorization(m)
#print(score)

def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p
p = 10**9+7 #割る数
N = 10 ** 6  # N は必要分だけ用意する
fact = [1, 1]  # fact[n] = (n! mod p)
factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1]  # factinv 計算用
for i in range(2, N + 1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)

ans=1
for item in score:
    c=item[1]
    ans*=cmb(n+c-1, c, p)
    #print(ans)
print(ans%p)

Submission status: Wrong Answer

Solution code:
n,m=map(int,input().split())

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

score=factorization(m)

def cmb(n, r, p):
    if (r < 0) or (n < r):
        return 0
    r = min(r, n - r)
    return fact[n] * factinv[r] * factinv[n-r] % p
p = 998244353 #割る数
N = 10 ** 6  # N は必要分だけ用意する
fact = [1, 1]  # fact[n] = (n! mod p)
factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
inv = [0, 1]  # factinv 計算用
for i in range(2, N + 1):
    fact.append((fact[-1] * i) % p)
    inv.append((-inv[p % i] * (p // i)) % p)
    factinv.append((factinv[-1] * inv[-1]) % p)

ans=0
for item in score:
    c=item[1]
    ans+=cmb(n+c-1, c, p)
print(ans%p)

Submission status: Wrong Answer

Solution code:
from collections import defaultdict,deque
from sys import stdin,setrecursionlimit
import heapq,bisect,math,itertools,string,queue,datetime,copy
setrecursionlimit(10**8)
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inpl(): return list(map(int, stdin.readline().split()))
import numpy as np

def prime_factor(N):#N**1/2より大きい素因数は高々一つ
    result = []
    for i in range(2,int(N**(1/2)+1)):
        count = 0
        while N%i ==0:
            count+=1
            N /= i
        if count:
            result.append((i,count))
    if N != 1:
        result.append((int(N),1))
    return result

N, M = inpl()
ls = prime_factor(M)
def tcomb(a,b):#b個をa種類に分ける重複組み合わせ 個数制限なし
    dp = np.full(b+1,1,dtype = np.int64)
    for _ in range(a-1):
        for j in range(b+1):
            if j == 0:
                dp[j] = 1
            else:
                dp[j] = (dp[j-1] + dp[j])%mod
    return dp[b]

ans = 1
for item in ls:
    ans *= (tcomb(N,item[1]))%mod

print(ans%mod)

Submission status: Wrong Answer

Solution code:
N,M=map(int,input().split())
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])
    if temp!=1:
        arr.append([temp, 1])
    if arr==[]:
        arr.append([n, 1])
    return arr
count=factorization(M)
for i in range(len(count)):
  for j in range(count[i][1]):
    M=M//count[i][0]
if M>1:
  count.append([M,1])
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
mod=10**9+7
for i,j in count:
  ans*=cmb(N-1+j,j)
  ans%=mod
print(ans)

Submission status: Wrong Answer

Solution code:
N,M=map(int,input().split())
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])
    if temp!=1:
        arr.append([temp, 1])
    if arr==[]:
        arr.append([n, 1])
    return arr
count=factorization(M)
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
mod=10**9+7
for i,j in count:
  ans*=cmb(N-1+j,j)
  ans%=mod
print(ans%mod)

Submission status: Wrong Answer

Solution code:
N,M=map(int,input().split())
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])
    if temp!=1:
        arr.append([temp, 1])
    if arr==[]:
        arr.append([n, 1])
    return arr
count=factorization(M)
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
mod=10**9+7
for i,j in count:
  ans*=cmb(N-1+j,j)
  ans%=mod
print(ans)

Submission status: Wrong Answer

Solution code:
N_MAX = 10**6
MOD = 10**9 + 7
fac, finv, inv = [0]*N_MAX ,[0]*N_MAX, [0]*N_MAX
def com_init():
    fac[0], fac[1] = 1, 1
    finv[0], finv[1] = 1, 1
    inv[1] = 1
    for i in range(2, N_MAX):
        fac[i] = fac[i - 1] * i % MOD
        inv[i] = MOD - inv[MOD%i] * (MOD // i) % MOD
        finv[i] = finv[i - 1] * inv[i] % MOD


def com(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


# 60 -> {2:2, 3:1, 5:1}
def factorization(n):
    pf_cnt = {}
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i == 0:
            cnt = 0
            while temp%i == 0:
                cnt += 1
                temp //= i
            pf_cnt[i] = cnt

    if temp != 1: pf_cnt[temp] = 1
    if not pf_cnt: pf_cnt[n] = 1

    return pf_cnt


def main():
    com_init()
    n, m = map(int, input().split())
    fac = factorization(m)
    prime_combs = []
    for prime, cnt in fac.items():
        prime_combs.append(com(n-1+cnt, cnt))

    ans = 1
    for c in prime_combs:
        ans*=c
        ans%=MOD

    print(ans)

if __name__ == "__main__":
    main()

Submission status: Wrong Answer

Solution code:
from collections import defaultdict

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

prime_list = defaultdict(int)
p = 2
while p <= 10**4.5+5:
    if m%p == 0:
        prime_list[p] += 1
        m //= p
    else:
        p += 1

if m > 1:
    prime_list[m] += 1

MOD=10**9+7

def comb(n, r): 
    if r<0 or r>n: 
        return 0
    r=min(r, n-r)
    res=1
    for i in range(r): 
        res=res*(n-i)%MOD*pow(i+1, MOD-2, MOD)%MOD
    return res

print(prime_list)

ans = 1
for k in prime_list.keys():
    ans *= comb(prime_list[k]+n-1, prime_list[k])
    ans %= MOD

print(ans)

Submission status: Wrong Answer

Solution code:
from collections import defaultdict

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

prime_list = defaultdict(int)
p = 2
while p <= 10**4.5+5:
    if m%p == 0:
        prime_list[p] += 1
        m //= p
    else:
        p += 1

MOD=10**9+7

def comb(n, r): 
    if r<0 or r>n: 
        return 0
    r=min(r, n-r)
    res=1
    for i in range(r): 
        res=res*(n-i)%MOD*pow(i+1, MOD-2, MOD)%MOD
    return res

ans = 1
for k in prime_list.keys():
    ans *= comb(prime_list[k]+n-1, prime_list[k])
    ans %= MOD

print(ans)