input stringlengths 20 127k | target stringlengths 20 119k | problem_id stringlengths 6 6 |
|---|---|---|
from collections import Counter
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
mod = 10**9+7 #出力の制限
N = 10**5+1000
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 )
n,m=list(map(int, input().split()))
mb=[]
while m>1:
for i in range(2,m+1):
if m%i==0:
mb.append(i)
m//=i
break
mb2=Counter(mb)
mblist=list()
for i in mb2:
a = cmb(mb2[i]+n-1,mb2[i],mod)
mblist.append(a)
ans=1
for i in mblist:
ans=(ans*i)%mod
print(ans) | from collections import Counter
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
mod = 10**9+7 #出力の制限
N = 10**5+1000
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 )
n,m=list(map(int, input().split()))
mb=[]
while m>1:
for i in range(2,int(m**0.5)+1):
if m%i==0:
mb.append(i)
m//=i
break
else:
mb.append(m)
m//=m
mb2=Counter(mb)
mblist=list()
for i in mb2:
a = cmb(mb2[i]+n-1,mb2[i],mod)
mblist.append(a)
ans=1
for i in mblist:
ans=(ans*i)%mod
print(ans) | p03253 |
from math import sqrt, ceil, factorial
from collections import defaultdict
def prime_factors(n):
i = 2
factors = defaultdict(int)
while i * i <= n:
if n % i:
i += 1
else:
n //= i
factors[i] += 1
if n > 1:
factors[n] += 1
return factors
N, M = [int(elem) for elem in input().split(' ')]
# 素因数分解
prime_numbers = prime_factors(M)
sum = 1
fac_N_m1 = factorial(N - 1)
for value in list(prime_numbers.values()):
bunshi = 1
saisho = value + N - 1
for _ in range(value):
bunshi *= saisho
saisho -= 1
sum *= (bunshi // factorial(value))
print((sum % (10**9 + 7)))
| from collections import defaultdict
def prime_factorize(num):
prime_numbers = defaultdict(int)
i = 2
while i * i <= num:
if num % i == 0:
while num % i == 0:
prime_numbers[i] += 1
num //= i
i += 1
if num != 1:
prime_numbers[num] += 1
return prime_numbers
MOD = 10**9 + 7
N, M = [int(elem) for elem in input().split()]
prime_numbers = prime_factorize(M)
num_sequences = 1
for exponent in list(prime_numbers.values()):
denomimator = 1
numerator = 1
for i in range(1, exponent + 1):
denomimator *= (N + exponent - i)
numerator *= i
num_sequences *= denomimator // numerator
num_sequences %= MOD
print(num_sequences)
| p03253 |
import sys
N, M = list(map(int, input().split()))
factor = {}
tmp = 2
while(M // tmp >= 1):
if(M % tmp != 0):
if(tmp == 2):
tmp += 1
else:
tmp += 2
continue
M = M // tmp
factor[tmp] = factor.get(tmp, 0) + 1
if(factor == {}):
print((1))
sys.exit()
ans = 1
max_a = 7 + 10 ** 9
max_value = max(list(factor.values()))
aho = {0: 1}
fact = {0: 1}
abc = {}
for i in range(1, max_value + 1):
# print(i)
aho[i] = ((aho[i - 1] * (i + N - 1)))
fact[i] = (fact[i - 1] * i)
abc[i] = (aho[i] // fact[i]) % max_a
# print(factor)
# print(aho, fact)
for i in list(factor.values()):
# print(i)
ans = (ans * abc[i]) % max_a
print(ans) | import sys
N, M = list(map(int, input().split()))
factor = {}
tmp = 2
while(M // tmp >= 1):
if(M % tmp != 0):
if(tmp == 2):
tmp += 1
elif(M // tmp < tmp):
tmp = M
else:
tmp += 2
continue
M = M // tmp
factor[tmp] = factor.get(tmp, 0) + 1
if(factor == {}):
print((1))
sys.exit()
ans = 1
max_a = 7 + 10 ** 9
max_value = max(list(factor.values()))
aho = {0: 1}
fact = {0: 1}
abc = {}
for i in range(1, max_value + 1):
# print(i)
aho[i] = ((aho[i - 1] * (i + N - 1)))
fact[i] = (fact[i - 1] * i)
abc[i] = (aho[i] // fact[i]) % max_a
# print(factor)
# print(aho, fact)
for i in list(factor.values()):
# print(i)
ans = (ans * abc[i]) % max_a
print(ans) | p03253 |
M = 10 ** 9 + 7
def main():
n, m = [int(s) for s in input().split()]
print((solve(m, n)))
def solve(m, n):
fs = list(factors(m))
table = dict()
table[1] = dict()
for f in fs:
table[1][f] = 1
h = 1
for _ in range(1, n.bit_length()):
row = dict()
for f in fs:
for g in fs:
if f * g > m:
break
row[f * g] = (row.get(f * g, 0) + table[h][f] * table[h][g]) % M
table[h * 2] = row
h *= 2
prev = { 1: 1 }
result = None
h = 1
for _ in range(n.bit_length()):
if n & h:
result = dict()
for f in list(prev.keys()):
for g in list(table[h].keys()):
if f * g <= m:
result[f * g] = (result.get(f * g, 0) + prev[f] * table[h][g]) % M
prev = result
h *= 2
return result[m]
def factors(n):
import itertools
tail = []
for i in itertools.count(1):
if i * i > n:
break
m, r = divmod(n, i)
if r == 0:
yield i
if m != i:
tail.append(m)
for i in tail[::-1]:
yield i
main()
| import sys
MOD = 10 ** 9 + 7
def main():
n, m = [int(s) for s in input().split()]
print((solve(m, n)))
def solve(m, n):
factors = list(get_prime_factors(m))
h = max((c for f, c in factors), default=0)
table = dict()
table[1] = [1 for _ in range(h + 1)]
i = 1
while i < n:
j = n & (i - 1)
table[i * 2] = [0 for _ in range(h + 1)]
if n & i != 0 and j != 0:
table[i + j] = [0 for _ in range(h + 1)]
for x in range(h + 1):
for y in range(h + 1 - x):
table[i * 2][x + y] = (table[i * 2][x + y] + table[i][x] * table[i][y]) % MOD
if n & i != 0 and j != 0:
table[i + j][x + y] = (table[i + j][x + y] + table[i][x] * table[j][y]) % MOD
if n & i == 0:
del table[i]
if n & i != 0 and j != 0:
del table[i]
del table[j]
i *= 2
ans = 1
for f, c in factors:
ans = ans * table[n][c] % MOD
return ans
def get_prime_factors(n):
import itertools
m = n
for i in itertools.count(2):
if i * i > m:
break
c = 0
while True:
x, y = divmod(m, i)
if y != 0:
break
c += 1
m = x
if c != 0:
yield i, c
if m != 1:
yield m, 1
main()
| p03253 |
import sys
MOD = 10 ** 9 + 7
def main():
n, m = [int(s) for s in input().split()]
print((solve(m, n)))
def solve(m, n):
factors = list(get_prime_factors(m))
h = max((c for f, c in factors), default=0)
table = dict()
table[1] = [1 for _ in range(h + 1)]
i = 1
while i < n:
j = n & (i - 1)
table[i * 2] = [0 for _ in range(h + 1)]
if n & i != 0 and j != 0:
table[i + j] = [0 for _ in range(h + 1)]
for x in range(h + 1):
for y in range(h + 1 - x):
table[i * 2][x + y] = (table[i * 2][x + y] + table[i][x] * table[i][y]) % MOD
if n & i != 0 and j != 0:
table[i + j][x + y] = (table[i + j][x + y] + table[i][x] * table[j][y]) % MOD
if n & i == 0:
del table[i]
if n & i != 0 and j != 0:
del table[i]
del table[j]
i *= 2
ans = 1
for f, c in factors:
ans = ans * table[n][c] % MOD
return ans
def get_prime_factors(n):
import itertools
m = n
for i in itertools.count(2):
if i * i > m:
break
c = 0
while True:
x, y = divmod(m, i)
if y != 0:
break
c += 1
m = x
if c != 0:
yield i, c
if m != 1:
yield m, 1
main()
| M = 10 ** 9 + 7
def main():
n, m = [int(s) for s in input().split()]
print((solve(m, n, 10 ** 9 + 7)))
def solve(m, n, mod):
r = 1
for _, c in get_prime_factors(m):
r = r * mod_comb(c + n - 1, c, mod) % mod
return r
def mod_comb(n, k, m):
r = 1
for i in range(1, k + 1):
r = r * (n - k + i) * mod_inv(i, m) % m
return r
def mod_inv(n, m):
r0, r1 = n, m
x, y, u, v = 1, 0, 0, 1
while r1:
k, r0, r1 = r0 // r1, r1, r0 % r1
x, y, u, v = u, v, x - k * u, y - k * v
if r0 != 1:
raise ValueError
return x
def get_prime_factors(n):
from itertools import count, takewhile
r = n
for i in takewhile(lambda x: x * x <= r, count(2)):
c = 0
while r % i == 0:
c += 1
r //= i
yield i, c
if r != 1:
yield r, 1
main()
| p03253 |
import math
def nCr(n,r):
return (math.factorial(n)) // (math.factorial(r)) // (math.factorial(n-r))
def nHr(n,r):
return nCr(n+r-1, r-1)
def prime(n): # nまでの素数を列挙
import math
num_list = [i + 1 for i in range(2,n,2)]
list_prime = [2]
limit = math.sqrt(n)
if n == 2:
return list_prime
else:
while True:
p = num_list[0]
if p >= limit:
return list_prime + num_list
list_prime.append(p)
num_list = [num for num in num_list if num % p != 0]
def primeFactorization(n):
import math
list_prime = prime(int(math.sqrt(n)))
i = 0
dict_pF = {}
dict_primeFactorization = {}
for pri in list_prime:
dict_pF[pri] = 0
while True:
if n == 1:
for key, value in list(dict_pF.items()):
if value != 0:
dict_primeFactorization[key] = value
return dict_primeFactorization
elif i >= len(list_prime):
dict_pF[n] = 1
for key, value in list(dict_pF.items()):
if value != 0:
dict_primeFactorization[key] = value
return dict_primeFactorization
p = list_prime[i]
if n % p == 0:
n //= p
dict_pF[p] += 1
continue
else:
i += 1
ans = 1
n,m = list(map(int, input().split()))
if m == 1:
ans = 1
else:
for factor,degree in list(primeFactorization(m).items()):
ans *= (nHr(degree,n)) % (10**9+7)
print((ans % (10**9+7)))
| import math
def fact(a,b):
ans = 1
while a != b:
ans *= a
a -= 1
return ans
def nCr(n,r):
return (fact(n,r)) // (math.factorial(n-r))
def nHr(n,r):
return nCr(n+r-1, r-1)
def prime(n): # nまでの素数を列挙
import math
num_list = [i + 1 for i in range(2,n,2)]
list_prime = [2]
limit = math.sqrt(n)
if n == 2:
return list_prime
else:
while True:
p = num_list[0]
if p >= limit:
return list_prime + num_list
list_prime.append(p)
num_list = [num for num in num_list if num % p != 0]
def primeFactorization(n):
import math
list_prime = prime(int(math.sqrt(n)))
i = 0
dict_pF = {}
dict_primeFactorization = {}
for pri in list_prime:
dict_pF[pri] = 0
while True:
if n == 1:
for key, value in list(dict_pF.items()):
if value != 0:
dict_primeFactorization[key] = value
return dict_primeFactorization
elif i >= len(list_prime):
dict_pF[n] = 1
for key, value in list(dict_pF.items()):
if value != 0:
dict_primeFactorization[key] = value
return dict_primeFactorization
p = list_prime[i]
if n % p == 0:
n //= p
dict_pF[p] += 1
continue
else:
i += 1
ans = 1
n,m = list(map(int, input().split()))
if m == 1:
ans = 1
else:
for factor,degree in list(primeFactorization(m).items()):
ans *= (nHr(degree,n)) % (10**9+7)
print((ans % (10**9+7)))
| p03253 |
#素因数分解
def soinsu_bunkai(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
# 組み合わせの総数 p=10**9+7 で割ったあまりを求める Satoooh Blog 2020/02/27 4分
"""n<10**7 , p は素数"""
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
# 初期入力
from collections import Counter
import sys
input = sys.stdin.readline #文字列では使わない
mod =10**9 +7
p =mod
N,M = list(map(int, input().split()))
a =soinsu_bunkai(M)
ans =1
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
#mod p における n の逆元の計算
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)
for i in list(a.values()):
x =cmb(N +i -1,i,mod)
ans *=x
print((ans %mod)) | #素因数分解
def soinsu_bunkai(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
# 組み合わせの総数 p=10**9+7 で割ったあまりを求める Satoooh Blog 2020/02/27 4分
"""n<10**7 , p は素数"""
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
# 初期入力
from collections import Counter
import sys
input = sys.stdin.readline #文字列では使わない
mod =10**9 +7
p =mod
N,M = list(map(int, input().split()))
a =soinsu_bunkai(M)
ans =1
n = 10 **5 +100 # 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
#mod p における n の逆元の計算
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)
for i in list(a.values()):
x =cmb(N +i -1,i,mod)
ans *=x
print((ans %mod)) | p03253 |
from collections import Counter
mod = 1000000007
# nの素因数分解
def prime(n):
d = Counter()
i = 2
while n != 1:
while n%i == 0:
n //= i
d[i] += 1
i += 1
return d
# xのn乗を計算する
def mod_pow(x, n):
if n == 0:
return 1
elif n % 2 == 0:
half_x = mod_pow(x, n // 2)
return half_x * half_x % mod
else:
return x * mod_pow(x, n-1) % mod
fact = [0] * 100099
inv = [0] * 100099
fact[0] = 1
inv[0] = 1
for k in range(1, 100099):
fact[k] = fact[k-1] * k % mod
inv[k] = mod_pow(fact[k], mod-2)
def nCr(n, r):
return fact[n] * inv[r] % mod * inv[n-r] % mod
def solve():
N, M = list(map(int, input().split()))
p = prime(M)
s = 1
for i in list(p.values()):
s *= nCr(i + N - 1, N - 1)
s %= mod
print(s)
solve() | from collections import Counter
mod = 1000000007
# nの素因数分解
def prime(n):
d = Counter()
i = 2
while i*i <= n:
while n%i == 0:
n //= i
d[i] += 1
i += 1
if n > 1:
d[n] += 1
return d
# xのn乗を計算する
def mod_pow(x, n):
if n == 0:
return 1
elif n % 2 == 0:
half_x = mod_pow(x, n // 2)
return half_x * half_x % mod
else:
return x * mod_pow(x, n-1) % mod
fact = [1] * 100100
inv = [1] * 100100
for k in range(1, 100100):
fact[k] = fact[k-1] * k % mod
inv[k] = mod_pow(fact[k], mod-2)
def nCr(n, r):
return fact[n] * inv[r] % mod * inv[n-r] % mod
def solve():
N, M = list(map(int, input().split()))
p = prime(M)
s = 1
for i in list(p.values()):
s *= nCr(i + N - 1, N - 1)
s %= mod
print(s)
solve()
| p03253 |
from collections import Counter
mod = 1000000007
# nの素因数分解
def prime(n):
d = Counter()
i = 2
while i*i <= n:
while n%i == 0:
n //= i
d[i] += 1
i += 1
if n > 1:
d[n] += 1
return d
# xのn乗を計算する
def mod_pow(x, n):
if n == 0:
return 1
elif n % 2 == 0:
half_x = mod_pow(x, n // 2)
return half_x * half_x % mod
else:
return x * mod_pow(x, n-1) % mod
fact = [1] * 100100
inv = [1] * 100100
for k in range(1, 100100):
fact[k] = fact[k-1] * k % mod
inv[k] = mod_pow(fact[k], mod-2)
def nCr(n, r):
return fact[n] * inv[r] % mod * inv[n-r] % mod
def solve():
N, M = list(map(int, input().split()))
p = prime(M)
s = 1
for i in list(p.values()):
s *= nCr(i + N - 1, N - 1)
s %= mod
print(s)
solve()
| from collections import Counter
mod = 1000000007
# nの素因数分解
def factor(n):
d = Counter()
i = 2
while i*i <= n:
while n%i == 0:
n //= i
d[i] += 1
i += 1
if n > 1:
d[n] += 1
return d
# xのn乗を計算する
def mod_pow(x, n):
if n == 0:
return 1
elif n % 2 == 0:
half = int(n / 2)
half_x = mod_pow(x, half)
return half_x * half_x % mod
else:
return x * mod_pow(x, n - 1) % mod
def nCr(n, r):
x = 1
r = min(r, n - r)
for i in range(r):
x *= n - i
x %= mod
x *= mod_pow(i + 1, mod - 2)
x %= mod
return x
def solve():
N, M = list(map(int, input().split()))
p = factor(M)
s = 1
for i in list(p.values()):
s *= nCr(i + N - 1, N - 1)
s %= mod
print(s)
solve() | p03253 |
import math
mod = 10**9 + 7
n, m = list(map(int, input().split()))
#mの素因数分解
#(prime, power)を要素としてもつ配列を返す関数を作る
def factorize(n):
fct = []
b, e = 2, 0
while b*b <= n:
while n%b == 0:
n //= b
e += 1
if e > 0:
fct.append((b, e))
b += 1
e = 0
if n > 1:
fct.append((n, 1))
return fct
def combinations_count(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
num = factorize(m)
ans = 1
for p in num:
ans *= (combinations_count(p[1]+n-1, p[1]) % mod)
print((ans%mod))
| import math
mod = 10**9 + 7
n, m = list(map(int, input().split()))
#mの素因数分解
#(prime, power)を要素としてもつ配列を返す関数を作る
def factorize(n):
fct = []
b, e = 2, 0
while b*b <= n:
while n%b == 0:
n //= b
e += 1
if e > 0:
fct.append((b, e))
b += 1
e = 0
if n > 1:
fct.append((n, 1))
return fct
num = factorize(m)
ans = 1
for p in num:
for i in range(p[1]):
ans *= n+i
for i in range(p[1]):
ans //= i+1
print((ans%mod))
| p03253 |
import math
def div(m):
d = {}
temp = int(math.sqrt(m))+1
for i in range(2, temp):
while m%i== 0:
m //= i
if i in d:
d[i] += 1
else:
d[i] = 1
if d == {}:
d[m] = 1
else:
if m in d:
d[m] += 1
elif m != 1:
d[m] =1
return d
n, m = list(map(int, input().split()))
if m == 1:
print((1))
exit()
#print(div(m))
from math import factorial
d = div(m)
#print(d)
ans = 1
for i in list(d.values()):
ans *= int(factorial(i+n-1)) // int(factorial(n-1)) // int(factorial(i))
ans %= 10**9+7
print(ans) | import math
def div(m):
d = {}
temp = int(math.sqrt(m))+1
for i in range(2, temp):
while m%i== 0:
m //= i
if i in d:
d[i] += 1
else:
d[i] = 1
if d == {}:
d[m] = 1
else:
if m in d:
d[m] += 1
elif m != 1:
d[m] =1
return d
n, m = list(map(int, input().split()))
if m == 1:
print((1))
exit()
#print(div(m))
from math import factorial
d = div(m)
#print(d)
ans = 1
for i in list(d.values()):
#ans *= int(factorial(i+n-1)) // int(factorial(n-1)) // int(factorial(i))
ans *= factorial(i+n-1) // factorial(n-1) // factorial(i)
ans %= 10**9+7
print(ans) | p03253 |
#!/usr/bin/env python3
#ABC110 D
import math
from collections import Counter
N,M = list(map(int,input().split()))
mod = 10**9 + 7
def factorize(n):
b = 2
fct = []
while b * b <= n:
while n % b == 0:
n //= b
fct.append(b)
b = b + 1
if n > 1:
fct.append(n)
return fct
def fast(x,n):
if n == 0:
return 1
elif n % 2 == 0:
return fast(x**2 % mod,n//2) % mod
elif n % 2:
return x*fast(x**2 % mod,n//2) % mod
cnt = list(Counter(factorize(M)).items())
ans = 1
for i,j in cnt:
ans *= math.factorial(j+N-1)
ans %= mod
ans *= fast(math.factorial(j),mod-2)
ans %= mod
ans *= fast(math.factorial(N-1),mod-2)
ans %= mod
print(ans)
| #!/usr/bin/env python3
#ABC110 D
import math
from collections import Counter
N,M = list(map(int,input().split()))
mod = 10**9 + 7
def factorize(n):
b = 2
fct = []
while b**2 <= n:
while n % b == 0:
n //= b
fct.append(b)
b += 1
if n > 1:
fct.append(n)
return fct
def fast(x,n):
if n == 0:
return 1
elif n % 2 == 0:
return fast(x**2 % mod,n//2) % mod
elif n % 2:
return x*fast(x**2 % mod,n//2) % mod
fact = [0]*(200001)
fact[0] = 1
for i in range(200000):
fact[i+1] = fact[i]*(i+1)
fact[i+1] %= mod
cnt = list(Counter(factorize(M)).items())
ans = 1
for i,j in cnt:
ans *= fact[j+N-1]
ans %= mod
ans *= fast(fact[j],mod-2)
ans %= mod
ans *= fast(fact[N-1],mod-2)
ans %= mod
print(ans)
| p03253 |
import math
N,M=list(map(int,input().split()))
dic={}
for i in range(2,int(M**0.5)+1):
if M%i==0:
dic.setdefault(i,1)
M//=i
while M%i==0:
dic[i]+=1
M//=i
if M==1: break
if M!=1: dic[M]=1
ans=1
for k in list(dic.keys()):
x=(dic[k]+N-1)
ans*=math.factorial(dic[k]+N-1)//(math.factorial(dic[k])*math.factorial(N-1))
print((ans%1000000007)) | import math
N,M=list(map(int,input().split()))
dic={}
for i in range(2,int(M**0.5)+1):
if M%i==0:
dic.setdefault(i,1)
M//=i
while M%i==0:
dic[i]+=1
M//=i
if M==1: break
if M!=1: dic[M]=1
ans=1
for k in list(dic.keys()):
x=dic[k]
tmp=1
for i in range (N,x+N):
tmp*=i
ans*=tmp//math.factorial(x)
ans%=1000000007
print((ans%1000000007)) | p03253 |
# -*- coding: utf-8 -*-
import math
def combinations_count(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
from collections import Counter
N, M = list(map(int, input().split()))
D = 1000000000 + 7
def primes(n):
primfac = []
d = 2
while d*d <= n:
while (n % d) == 0:
primfac.append(d) # supposing you want multiple factors repeated
n //= d
d += 1
if n > 1:
primfac.append(n)
return primfac
f = primes(M)
cntr = Counter(f)
ans = 1
for k,v in list(cntr.items()):
ans *= combinations_count(v+N-1,v) %D
print((ans%D))
| # -*- coding: utf-8 -*-
import math
# 高速 組み合わせ
def C(n, r):
a = 1
b = 1
for i in range(r):
a = a*(n-i)
b = b*(r-i)
return((a//b))
from collections import Counter
N, M = list(map(int, input().split()))
D = 1000000000 + 7
def primes(n):
primfac = []
d = 2
while d*d <= n:
while (n % d) == 0:
primfac.append(d) # supposing you want multiple factors repeated
n //= d
d += 1
if n > 1:
primfac.append(n)
return primfac
f = primes(M)
cntr = Counter(f)
ans = 1
for k,v in list(cntr.items()):
ans *= C(v+N-1,v) %D
print((ans%D))
| p03253 |
from collections import Counter
from math import factorial
Q = 10**9+7
def primes(n):
primfac = [0]
d = 2
while d*d <= n:
while n%d == 0:
primfac[-1] += 1
n //= d
d += 1
if primfac[-1] != 0:
primfac.append(0)
if n > 1:
if primfac[-1] == 0:
primfac[-1] += 1
else:
primfac.append(1)
return primfac
def combination(a,b):
return ( (factorial(a)//factorial(b))//factorial(a-b))%Q
N, M = list(map( int, input().split()))
C = primes(M)
ans = 1
if N == 1:
print((1))
else:
for x in C:
ans = (ans * combination(x+N-1,N-1))%Q
print(ans) | from math import factorial
Q = 10**9+7
def primes(n):
primfac = [0]
d = 2
while d*d <= n:
while n%d == 0:
primfac[-1] += 1
n //= d
d += 1
if primfac[-1] != 0:
primfac.append(0)
if n > 1:
if primfac[-1] == 0:
primfac[-1] += 1
else:
primfac.append(1)
return primfac
N, M = list(map( int, input().split()))
C = primes(M)
ans = 1
if N == 1:
print((1))
else:
for x in C:
for i in range(x):
ans *= N+i
ans //= factorial(x)
ans = ans%Q
print(ans)
| p03253 |
import math
MOD=10**9+7
def powmod(a,p):
if p==0:
return 1
elif p==1:
return a
else:
pow2=powmod(a,p//2)
if p%2==0:
return (pow2**2)%MOD
else:
return (a*pow2**2)%MOD
def invmod(a):
return powmod(a,MOD-2)
def comb_mod(n,r):
nPr=1
fact_r=1
for i in range(r):
nPr*=n-i
nPr%=MOD
fact_r*=r-i
fact_r%=MOD
return (nPr*invmod(fact_r))%MOD
N,M=list(map(int,input().split()))
fact={}
for i in range(2,int(math.sqrt(M))+1):
if M==1:
break
while(M%i==0):
M//=i
if not i in fact:
fact[i]=1
else:
fact[i]+=1
if M!=1:
fact[M]=1
#print(fact)
answer=1
for r in list(fact.values()):
answer*=comb_mod(N+r-1,r)
answer%=MOD
print(answer) | import math
MOD=10**9+7
def comb(n,r):
nPr=1
fact_r=1
for i in range(r):
nPr*=n-i
fact_r*=r-i
return nPr//fact_r
N,M=list(map(int,input().split()))
fact={}
for i in range(2,int(math.sqrt(M))+1):
if M==1:
break
while(M%i==0):
M//=i
if not i in fact:
fact[i]=1
else:
fact[i]+=1
if M!=1:
fact[M]=1
#print(fact)
answer=1
for r in list(fact.values()):
answer*=comb(N+r-1,r)
answer%=MOD
print(answer) | p03253 |
#!/usr/bin/env python3
import sys
from math import *
from itertools import *
from collections import *
from functools import *
from operator import *
try:
from math import gcd
except Exception:
from fractions import gcd
MOD = 1000000007 # type: int
def prime_table(n):
rn = int(ceil(sqrt(n)))
t = [True] * (rn + 1)
t[0] = False
t[1] = False
i = 2
while i * i <= n:
for ii in range(2 * i, rn + 1, i):
t[ii] = False
i += 1
return [x for x, i in enumerate(t) if i == True]
def combination(n, m):
return reduce(mul, list(range(n, n - m, -1)), 1) // factorial(m)
def solve(N: int, M: int):
fs = defaultdict(int)
for p in prime_table(M):
while (M % p) == 0:
fs[p] += 1
M //= p
if M != 1:
fs[M] = 1
ret = 1
for c in list(fs.values()):
ret *= combination(c + N - 1, c)
return ret % MOD
def main():
def iterate_tokens():
for line in sys.stdin:
for word in line.split():
yield word
tokens = iterate_tokens()
N = int(next(tokens)) # type: int
M = int(next(tokens)) # type: int
result = solve(N, M)
print(result)
if __name__ == '__main__':
main()
| #!/usr/bin/env python3
import sys
from math import *
from itertools import *
from collections import *
from functools import *
from operator import *
try:
from math import gcd
except Exception:
from fractions import gcd
MOD = 1000000007 # type: int
def prime_table(n):
t = [True] * (n + 1)
t[0] = False
t[1] = False
for p in range(2, n + 1, 2):
if n < p ** 2:
break
if t[p]:
for i in range(p * p, n + 1, 2 * p):
t[i] = False
return [2] + [p for p in range(3, n + 1, 2) if t[p]]
def pow_mod(a, k, M):
if k == 0:
return 1
t = pow_mod(a, k // 2, M)
res = (t * t) % M
if k % 2 == 1:
res = (res * a) % M
return res
def inv_mod(a, M):
return pow_mod(a, M - 2, M)
def fact_mod(a, M):
ret = 1
for i in range(2, a + 1):
ret = (ret * i) % M
return ret
def perm_mod(n, m, M):
ret = 1
for i in range(n, n - m, -1):
ret = (ret * i) % M
return ret
def comb_mod(n, m, M):
return (perm_mod(n, m, M) * inv_mod(fact_mod(m, M), M)) % M
def solve(N: int, M: int):
fs = defaultdict(int)
for p in prime_table(int(M ** 0.5) + 1):
while (M % p) == 0:
fs[p] += 1
M //= p
if M != 1:
fs[M] = 1
ret = 1
for c in list(fs.values()):
ret = (ret * comb_mod(c + N - 1, c, MOD)) % MOD
return ret
def main():
def iterate_tokens():
for line in sys.stdin:
for word in line.split():
yield word
tokens = iterate_tokens()
N = int(next(tokens)) # type: int
M = int(next(tokens)) # type: int
result = solve(N, M)
print(result)
if __name__ == '__main__':
main()
| p03253 |
import math
def prime_factors(n):
i = 2
factors = []
while i * i <= n:
if n % i:
i += 1
else:
n //= i
factors.append(i)
if n > 1:
factors.append(n)
return factors
a = input().split()
a = [int(i) for i in a]
num = dict()
for i in prime_factors(a[1]):
if i not in num:
num[i] = 1
else:
num[i] += 1
ans = 1
for j in list(num.values()):
ans *= (math.factorial(j + a[0] - 1)//(math.factorial(a[0] - 1)* math.factorial(j)))
ans %= (10**9 + 7)
print(ans) | import math
def prime_factors(n):
i = 2
factors = []
while i * i <= n:
if n % i:
i += 1
else:
n //= i
factors.append(i)
if n > 1:
factors.append(n)
return factors
def egcd(a, b):
if a == 0:
return (b, 0, 1)
else:
g, y, x = egcd(b % a, a)
return (g, x - (b // a) * y, y)
def modinv(a, m):
g, x, y = egcd(a, m)
if g != 1:
raise Exception('modular inverse does not exist')
else:
return x % m
def factorial(n):
num = 1
while n >= 1:
num = (num * n) % 1000000007
n = n - 1
return num
a = input().split()
a = [int(i) for i in a]
num = dict()
for i in prime_factors(a[1]):
if i not in num:
num[i] = 1
else:
num[i] += 1
ans = 1
for j in list(num.values()):
ans *= factorial(j + a[0] - 1)
ans %= (10**9 + 7)
inv = modinv((factorial(a[0] - 1)* factorial(j)), 1000000007)
ans *= inv
ans %= (10**9 + 7)
print(ans) | p03253 |
import math
import collections
N, M = input().strip().split(' ')
N, M = [int(N), int(M)]
#階乗
def combinations_count(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
#素因数分解
def prime_factors(n):
i = 2
factors = []
while i * i <= n:
if n % i:
i += 1
else:
n //= i
factors.append(i)
if n > 1:
factors.append(n)
return factors
C = collections.Counter(prime_factors(M))
res = 1
for c in list(C.items()):
#print(c[0], c[1])
res *= combinations_count((c[1] + N - 1), c[1])
print((res % (1000000007))) | N, M = [int(_) for _ in input().split()]
mod = 10 ** 9 + 7
MAX_N = 10 ** 5 + 100
#階乗
def calc_factorial(max_i):
factorial = [1] * max_i
for i in range(1, max_i):
factorial[i] = (i * factorial[i - 1]) % mod
return factorial
#素因数分解
def calc_factorization(n):
factorization = {}
for i in range(2, int(n ** 0.5) + 1):
if n % i == 0:
factorization[i] = 1
n = n // i
while n % i == 0:
factorization[i] += 1
n = n // i
if n > 1:
factorization[n] = 1
return factorization
#組み合わせ
def comb(factorial, n, k, mod):
a = factorial[n] % mod
b = (factorial[k] * factorial[n - k]) % mod
b_ = pow(b, mod - 2, mod)
return (a * b_) % mod
C = calc_factorization(M)
#階乗を計算しておく
factorial = calc_factorial(MAX_N)
res = 1
for c in list(C.items()):
res *= comb(factorial, (c[1] + N - 1), c[1], mod) #combinations_count(factorial, (c[1] + N - 1), c[1], mod)
print((res % mod)) | p03253 |
from collections import Counter
from math import sqrt
#f_listとf_r_listの要素数は状況に応じて変えよう
MOD = (10 ** 9) + 7
list_size = 3 * (10 ** 5)
f_list = [1] * list_size
f_r_list = [1] * list_size
for i in range(list_size - 1):
f_list[i + 1] = int((f_list[i] * (i + 2)) % MOD)
def power(n, x):
if x == 1:
return n
elif x % 2 == 0:
return power(int((n * n) % MOD), int(x / 2))
else:
return int((n * power(n, x - 1)) % MOD)
f_r_list[-1] = power(f_list[-1], MOD - 2)
for i in range(2, list_size + 1):
f_r_list[-i] = int((f_r_list[-i + 1] * (list_size + 2 - i)) % MOD)
def comb(n, r):
if n < r:
return 0
elif n == 0 or r == 0 or n == r:
return 1
else:
return (((f_list[n - 1] * f_r_list[n - r - 1]) % MOD) * f_r_list[r - 1]) % MOD
#prime = [2]
def is_prime(i):
if i == 1:
return False
#global prime
for j in range(2, int(sqrt(i)) + 1):
if i % j == 0:
return False
return True
n, m = list(map(int, input().split()))
prime_factor = Counter()
for i in range(2, int(sqrt(m)) + 1):
if m % i == 0:
prime_factor[i] += 1
m = m // i
while m % i == 0:
prime_factor[i] += 1
m = m // i
if is_prime(m):
prime_factor[m] += 1
break
ans = 1
for i in list(prime_factor.values()):
ans *= comb(n + i - 1, i)
ans %= MOD
print(ans)
| from collections import Counter
from math import sqrt
#f_listとf_r_listの要素数は状況に応じて変えよう
MOD = (10 ** 9) + 7
list_size = 3 * (10 ** 5)
f_list = [1] * list_size
f_r_list = [1] * list_size
for i in range(list_size - 1):
f_list[i + 1] = int((f_list[i] * (i + 2)) % MOD)
def power(n, x):
if x == 1:
return n
elif x % 2 == 0:
return power(int((n * n) % MOD), int(x / 2))
else:
return int((n * power(n, x - 1)) % MOD)
f_r_list[-1] = power(f_list[-1], MOD - 2)
for i in range(2, list_size + 1):
f_r_list[-i] = int((f_r_list[-i + 1] * (list_size + 2 - i)) % MOD)
def comb(n, r):
if n < r:
return 0
elif n == 0 or r == 0 or n == r:
return 1
else:
return (((f_list[n - 1] * f_r_list[n - r - 1]) % MOD) * f_r_list[r - 1]) % MOD
def is_prime(i):
if i == 1:
return False
for j in range(2, int(sqrt(i)) + 1):
if i % j == 0:
return False
return True
n, m = list(map(int, input().split()))
prime_factor = Counter()
for i in range(2, int(sqrt(m)) + 1):
if m % i == 0:
prime_factor[i] += 1
m = m // i
while m % i == 0:
prime_factor[i] += 1
m = m // i
if is_prime(m):
prime_factor[m] += 1
break
ans = 1
for i in list(prime_factor.values()):
ans *= comb(n + i - 1, i)
ans %= MOD
print(ans)
| p03253 |
# -*- coding: utf-8 -*-
'''Snippets for prime.
Available functions:
- is_included: Determine whether it is a prime number.
- generate: Generate a list of prime numbers using sieve of Eratosthenes.
'''
class Prime(object):
'''Represents a snippet for prime numbers.
'''
def __init__(self, number):
self.number = number
self._values = []
def is_included(self) -> bool:
'''Determine whether it is a prime number.
Args:
number: Int of number (greater than 0).
Returns:
True if the input number was prime.
False if the input number was not prime.
See:
https://qiita.com/srtk86/items/874639e361917e5016d4
https://docs.python.org/ja/3/library/2to3.html?highlight=isinstance#2to3fixer-isinstance
'''
from math import sqrt
if (self.number <= 1) or (isinstance(self.number, float)):
return False
for i in range(2, int(sqrt(self.number)) + 1):
if self.number % i == 0:
return False
return True
def generate(self) -> list:
'''Generate a list of prime numbers using sieve of Eratosthenes.
Returns:
A list of prime numbers that is eqaul to or less than the input
number.
Landau notation: O(n log log n)
See:
https://beta.atcoder.jp/contests/abc110/submissions/3254947
'''
if self._values:
return self._values
is_met = [True for _ in range(self.number + 1)]
is_met[0] = False
is_met[1] = False
for i in range(2, self.number + 1):
if is_met[i]:
self._values.append(i)
for j in range(2 * i, self.number + 1, i):
is_met[j] = False
return self._values
def count_combinations(n, k, mod):
ans = 1
for i in range(1, k + 1):
ans *= n - i + 1
ans %= mod
ans *= pow(i, mod - 2, mod)
ans %= mod
return ans
def main():
from math import sqrt
n, m = list(map(int, input().split()))
_prime = Prime(int(sqrt(m)) + 1)
primes = _prime.generate()
mod = 10 ** 9 + 7
ans = 1
for prime in primes:
count = 0
while m % prime == 0:
count += 1
m //= prime
ans *= count_combinations(n + count - 1, count, mod)
ans %= mod
if m != 1:
ans *= count_combinations(n, 1, mod)
ans %= mod
print(ans)
if __name__ == '__main__':
main()
| # -*- coding: utf-8 -*-
mod = 10 ** 9 + 7
'''Snippets for combination.
Available functions:
- count_combination: Count the total number of combinations.
'''
def count_combination(n: int, r: int, mod: int = 10 ** 9 + 7) -> int:
'''Count the total number of combinations.
nCr % mod.
Args:
n : Elements. Int of number (greater than 1).
r : The number of r-th combinations. Int of number (greater than 0).
mod : Modulo. The default is 10 ** 9 + 7.
Returns:
The total number of combinations.
Landau notation: O(n)
See:
https://qiita.com/derodero24/items/91b6468e66923a87f39f
'''
if r > (n - r):
return count_combination(n, n - r)
if r == 0 or r == n:
return 1
if r == 1:
return n
multiple = 1
division = 1
for i in range(r):
multiple *= n - i
division *= i + 1
multiple %= mod
division %= mod
return multiple * pow(division, mod - 2, mod) % mod
def solve(n: int, m: int):
from math import sqrt
ans = 1
remain = m
for j in range(2, int(sqrt(m)) + 1):
if remain % j == 0:
count = 0
while remain % j == 0:
count += 1
remain //= j
ans *= count_combination(n + count - 1, n - 1)
ans %= mod
if remain != 1:
ans *= count_combination(n, 1)
ans %= mod
return ans
def main():
n, m = list(map(int, input().split()))
# See:
# https://www.youtube.com/watch?v=gdQxKESnXKs
print((solve(n, m)))
if __name__ == '__main__':
main()
| p03253 |
from math import floor, sqrt
from collections import defaultdict
def factors(n):
d = defaultdict(int)
for i in range(2,floor(sqrt(n))+1):
while n % i == 0:
n //= i
d[i] += 1
if n == 1:
break
if n != 1:
d[n] += 1
return d
def inv(x, mod):
k = mod - 2
ret = 1
while k > 0:
if k&1:
ret = (ret*x) % mod
x = (x*x) % mod
k >>= 1
return ret
N, M = list(map(int,input().split()))
mod = 10**9+7
dic = factors(M)
K = len(dic)
SIZE = N+max(dic.values()) if list(dic.values()) else N
fact = [None]*(SIZE+1)
finv = [None]*(SIZE+1)
fact[0] = 1
for i in range(1,SIZE+1):
fact[i] = (fact[i-1]*i) % mod
finv[SIZE] = inv(fact[SIZE], mod=mod)
for i in range(SIZE, 0, -1):
finv[i-1] = (finv[i]*i) % mod
def comb(n,k):
tmp = (finv[k]*finv[n-k]) % mod
return (fact[n]*tmp) % mod
ans = 1
for p in dic:
ans = (ans*comb(dic[p]+N-1, dic[p])) % mod
print(ans) | from math import floor, sqrt
from collections import defaultdict
N,M = list(map(int,input().split()))
d = defaultdict(int)
for i in range(2, floor(sqrt(M))+1):
while M % i == 0:
d[i] += 1
M //= i
if M != 1:
d[M] += 1
def comb(n,k):
if k == 0:
return 1
return comb(n-1,k-1) * n // k
ans = 1
for e in list(d.values()):
ans *= comb(N+e-1, e)
print((ans % (10**9+7))) | p03253 |
# 素数リスト生成
def sieve(x):
if x < 2: return []
primes = [i for i in range(x)]
primes[1] = 0
for p in primes:
if p > x ** (1/2): break
if p == 0: continue
for np in range(2 * p, x, p): primes[np] = 0
return [p for p in primes if p != 0]
PS = sieve(10**7)
# 素因数分解
def factorint(x):
d = {}
for k in PS:
if(x % k== 0):
m = 1
while(x % (k**m) == 0):
m += 1
d[k] = m - 1
x = x / (k ** (m - 1))
if x == 1:
break
return d
n, m = list(map(int, input().split()))
f = factorint(m)
idx = [i for i in list(f.values())]
def fact(n):
ret = 1
for i in range(1, n + 1):
ret *= i
return ret
def com(n, r):
if n - r < r: r = n - r
ret = 1
for i in range(n-r+1, n+1):
ret *= i
for j in range(1, r+1):
ret //= j
return ret
ans = 1
for i in range(len(idx)):
ans *= com(idx[i] + n - 1, n - 1) % (10 ** 9 + 7)
print((ans % (10 ** 9 + 7))) | # 素数リスト生成
def sieve(x):
if x < 2: return []
primes = [i for i in range(x)]
primes[1] = 0
for p in primes:
if p > x ** (1/2): break
if p == 0: continue
for np in range(2 * p, x, p): primes[np] = 0
return [p for p in primes if p != 0]
PS = sieve(10**6)
# 素因数分解
def factorint(x):
d = {}
for k in PS:
if(x % k== 0):
m = 1
while(x % (k**m) == 0):
m += 1
d[k] = m - 1
x = x / (k ** (m - 1))
if x == 1:
break
return d
n, m = list(map(int, input().split()))
f = factorint(m)
idx = [i for i in list(f.values())]
# 10^6より大きい素因数があったときの処理
re = 1
for k, v in list(f.items()):
re *= k**v
if m // re != 1:
idx.append(1)
def fact(n):
ret = 1
for i in range(1, n + 1):
ret *= i
return ret
def com(n, r):
if n - r < r: r = n - r
ret = 1
for i in range(n-r+1, n+1):
ret *= i
for j in range(1, r+1):
ret //= j
return ret
ans = 1
for i in range(len(idx)):
ans *= com(idx[i] + n - 1, n - 1) % (10 ** 9 + 7)
print((ans % (10 ** 9 + 7))) | p03253 |
import sys
MOD = 10 ** 9 + 7
def make_table(size=10**6, p=MOD):
fac = [None] * (size + 1)
fac[0] = 1
for i in range(size):
fac[i+1] = fac[i] * (i + 1) % p
ifac = [None] * (size + 1)
ifac[size] = pow(fac[size], p-2, p)
for i in range(size, 0, -1):
ifac[i-1] = ifac[i] * i % p
return fac, ifac
fac, ifac = make_table()
def comb(n, r, mod=MOD):
if r > n or r < 0:
return 0
return fac[n] * ifac[r] % mod * ifac[n-r] % mod
from collections import defaultdict
from math import floor, sqrt
def prime_factorize(n):
res = defaultdict(int)
while n % 2 == 0:
res[2] += 1
n //= 2
if n == 1:
return res
for i in range(3, floor(sqrt(n))+1, 2):
while n % i == 0:
res[i] += 1
n //= i
if n == 1:
return res
res[n] += 1
return res
n, m = list(map(int, sys.stdin.readline().split()))
def main():
pfacts = prime_factorize(m)
res = 1
for v in list(pfacts.values()):
res *= comb(n-1+v, v)
res %= MOD
return res
if __name__ == '__main__':
ans = main()
print(ans) | import sys
MOD = 10 ** 9 + 7
def make_table(size=10**6, p=MOD):
fac = [None] * (size + 1)
fac[0] = 1
for i in range(size):
fac[i+1] = fac[i] * (i + 1) % p
ifac = [None] * (size + 1)
ifac[size] = pow(fac[size], p-2, p)
for i in range(size, 0, -1):
ifac[i-1] = ifac[i] * i % p
return fac, ifac
fac, ifac = make_table(10**5+30)
def comb(n, r, mod=MOD):
if r > n or r < 0:
return 0
return fac[n] * ifac[r] % mod * ifac[n-r] % mod
from collections import defaultdict
from math import floor, sqrt
def prime_factorize(n):
res = defaultdict(int)
while n % 2 == 0:
res[2] += 1
n //= 2
if n == 1:
return res
for i in range(3, floor(sqrt(n))+1, 2):
while n % i == 0:
res[i] += 1
n //= i
if n == 1:
return res
res[n] += 1
return res
n, m = list(map(int, sys.stdin.readline().split()))
def main():
pfacts = prime_factorize(m)
res = 1
for v in list(pfacts.values()):
res *= comb(n-1+v, v)
res %= MOD
return res
if __name__ == '__main__':
ans = main()
print(ans) | p03253 |
import math
n, m=list(map(int, input().split()))
t = {}
a = int(math.sqrt(m))
s=0
line = [2, 3] + [i%2*2 + i//2 * 6 + 5 for i in range(a//3)]
while s==0:
for i in line:
cnt = 0
while m%i==0:
m=m//i
cnt += 1
if cnt>0:
t[i]=cnt
if m==1:
s=1
break
def combi(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
out=1
for tk in list(t.keys()):
out *= combi(t[tk]+n-1, n-1)
print((out%(1000000007))) | import math
n, m=list(map(int, input().split()))
t = {}
a = int(math.sqrt(m))
s=0
line = [2, 3] + [i%2*2 + i//2 * 6 + 5 for i in range(a)]
# line = [2] + list(range(3, m+2, 2))
for i in line:
# for i in range(2, m+2, 2):
# print(i)
cnt = 0
while m%i==0:
m=m//i
cnt += 1
if cnt>0:
t[i]=cnt
if m==1:
break
if m!=1:
t[m]=1
def combi(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
out=1
for tk in list(t.keys()):
out *= combi(t[tk]+n-1, n-1)
# out = out%(1000000007)
print((out%(1000000007))) | p03253 |
import math
N, M = list(map(int, input().split()))
MOD = 10 ** 9 + 7
def factoring(k): #kを因数分解し、素因数とその個数を辞書に入れて返す。
dic = dict()
n = int(math.sqrt(k))+2
for i in range(2, n):
count = 0
while k%i == 0:
count += 1
k = k//i
if count != 0:
dic[i] = count
if k != 1:
dic[k] = 1
return dic
def conbination(n, r): #nCrを求める
# nCr = n! //(r! * (n-r)!)
import math
return (math.factorial(n) //(math.factorial(r) * math.factorial(n-r)))%MOD
dic = factoring(M)
ans = 1
for i in dic:
ans = (ans * conbination(dic[i]+N-1, dic[i]))%MOD
print (ans)
| MOD = 10 ** 9 + 7
N, M = list(map(int, input().split()))
def factoring(k): #kを因数分解し、素因数とその個数を辞書に入れて返す。
import math
dic = dict()
n = int(math.sqrt(k))+2
for i in range(2, n):
count = 0
while k%i == 0:
count += 1
k = k//i
if count != 0:
dic[i] = count
if k != 1: #sqrt(k)までチェックしてもkが1になっていない --> kが素因数
dic[k] = 1
return dic
class Factorial:
def __init__(self, n, mod):
self.f = [1]
self.mod = mod
for j in range(1, n + 1):
self.f.append(self.f[-1] * j % mod)
self.i = [pow(self.f[-1], mod - 2, mod)]
for j in range(n, 0, -1):
self.i.append(self.i[-1] * j % mod)
self.i.reverse()
def factorial(self, j):
return self.f[j]
def ifactorial(self, j):
return self.i[j]
def comb(self, n, k):
return self.f[n] * self.i[n - k] % self.mod * self.i[k] % self.mod if n >= k else 0
C = Factorial(N + 100, MOD).comb
ans = 1
dic = factoring(M)
for tmp in dic:
# print (tmp, dic[tmp])
ans *= C(dic[tmp] + N - 1, dic[tmp])
ans %= MOD
print (ans)
| p03253 |
import math
from collections import defaultdict
n, m = [int(i) for i in input().split()]
A = defaultdict(int)
p = 10 ** 9 + 7
if m == 1:
print((1))
exit()
def fact(n, p=10**9 + 7):
f = [1]
for i in range(1, n+1):
f.append(f[-1]*i%p)
return f
def invfact(n, f, p=10**9 + 7):
inv = [pow(f[n], p-2, p)]
for i in range(n, 0, -1):
inv.append(inv[-1]*i%p)
return inv[::-1]
f = fact(30+10**5)
invf = invfact(30+10**5, f)
def comb(a, b):
return f[a] * invf[b] * invf[a-b] % p
i = 2
while m != 1 and i <= math.sqrt(m) + 1:
while m % i == 0:
m //= i
A[i] += 1
i += 1
if not A:
print(n)
exit()
if m != 1:
A[m] = 1
n -= 1
ans = 1
for v in list(A.values()):
ans *= comb(v+n, n)
ans %= p
print(ans) | from math import sqrt
from collections import defaultdict
n, m = [int(i) for i in input().split()]
A = defaultdict(int)
p = 10 ** 9 + 7
def fact(n, p=10**9 + 7):
f = [1]
for i in range(1, n+1):
f.append(f[-1]*i%p)
return f
def invfact(n, f, p=10**9 + 7):
inv = [pow(f[n], p-2, p)]
for i in range(n, 0, -1):
inv.append(inv[-1]*i%p)
return inv[::-1]
f = fact(30+10**5)
invf = invfact(30+10**5, f)
def comb(a, b):
return f[a] * invf[b] * invf[a-b] % p
i = 2
while m != 1 and i <= sqrt(m) + 1:
while m % i == 0:
m //= i
A[i] += 1
i += 1
if m != 1:
A[m] = 1
n -= 1
ans = 1
for v in list(A.values()):
ans *= comb(v+n, n)
ans %= p
print(ans) | p03253 |
import math
n, m = list(map(int, input().split()))
mod = 10**9 + 7
b = []
c = int(math.sqrt(m))
for i in range(2, c+2):
count = 0
while m % i == 0:
count += 1
m = m // i
b.append(count)
if m > 1:
b.append(1)
fac = [1, 1]
inv = [1, 1]
finv = [1, 1]
for i in range(2, n + max(b)+3):
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
ans = 1
for i in b:
ans *= nck(n-1+i, i)
ans %= mod
print(ans) | import math
n, m = list(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)
| p03253 |
import math
from collections import defaultdict
n, m = list(map(int, input().split()))
def prime_factors(n):
i = 2
factors = []
while i * i <= n:
if n % i:
i += 1
else:
n //= i
factors.append(i)
if n > 1:
factors.append(n)
return factors
pr = prime_factors(m)
di = {}
di = defaultdict(int)
for i in pr:
while m % i == 0:
m = m // i
di[i] += 1
def comb(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
ans = 1
mod = 10 ** 9 + 7
for i in di:
ans = ans * comb(di[i] + n - 1, di[i]) % mod
print(ans) | import math
from collections import defaultdict
n, m = list(map(int, input().split()))
def prime_factors(n):
i = 2
factors = []
while i * i <= n:
if n % i:
i += 1
else:
n //= i
factors.append(i)
if n > 1:
factors.append(n)
return factors
pr = prime_factors(m)
di = {}
di = defaultdict(int)
for i in pr:
while m % i == 0:
m = m // i
di[i] += 1
"""def comb(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))"""
mod = 10 ** 9 + 7
MAX_N = 10 ** 5 + 100
factorial = [1] * MAX_N
def calc_factorial():
for i in range(1, MAX_N):
factorial[i] = i * factorial[i - 1] % mod
def comb(n, k):
a = factorial[n] % mod
b = (factorial[k] * factorial[n - k]) % mod
b_ = pow(b, mod - 2, mod)
return (a * b_) % mod
# 階乗を用意
calc_factorial()
ans = 1
for i in di:
ans = ans * comb(di[i] + n - 1, di[i]) % mod
print(ans) | p03253 |
# ABC110d
import sys
from collections import Counter
import math
input = sys.stdin.readline
sys.setrecursionlimit(10**6)
n, m = list(map(int, input().split()))
MOD = 10**9+7
def prime_factorize(n):
a = []
while n % 2 == 0:
a.append(2)
n //= 2
f = 3
while f * f <= n:
if n % f == 0:
a.append(f)
n //= f
else:
f += 2
if n != 1:
a.append(n)
return a
def combinations_count(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def combinations_with_replacement_count(n, r):
return combinations_count(n + r - 1, r)
ans = 1
pr = Counter(prime_factorize(m))
for i in list(pr.values()):
# print(i)
t = combinations_count(n + i - 1, i)
# print(t)
ans = ans*t % MOD
# print(pr)
# print(len(pr))
print(ans) | # ABC110d
import sys
from collections import Counter
import math
input = sys.stdin.readline
sys.setrecursionlimit(10**6)
n, m = list(map(int, input().split()))
MOD = 10**9+7
def prime_factorize(n):
a = []
while n % 2 == 0:
a.append(2)
n //= 2
f = 3
while f * f <= n:
if n % f == 0:
a.append(f)
n //= f
else:
f += 2
if n != 1:
a.append(n)
return a
dp = dict()
def combinations_count(n, r):
if dp.get(n) != None and dp.get(n).get(r) != None:
return dp[n][r]
if dp.get(n) == None:
dp[n] = dict()
dp[n].update({r: math.factorial(
n) // (math.factorial(n - r) * math.factorial(r))})
return dp[n][r]
def combinations_with_replacement_count(n, r):
return combinations_count(n + r - 1, r)
ans = 1
pr = Counter(prime_factorize(m))
for i in list(pr.values()):
# print(i)
t = combinations_count(n + i - 1, i)
# print(t)
ans = ans*t % MOD
# print(pr)
# print(len(pr))
print(ans) | p03253 |
N,M = list(map(int,input().split()))
prime = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499,503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823,1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229,4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507,5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823,6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171,8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479,9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171,11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577,12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, 13997,13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401,15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569, 15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661, 15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, 16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, 16427, 16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, 16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889, 16901,16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, 16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, 17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, 17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 17321, 17327, 17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519, 17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599, 17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737, 17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863, 17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939, 17957, 17959, 17971, 17977, 17981, 17987, 17989, 18013, 18041, 18043, 18047, 18049, 18059, 18061, 18077, 18089, 18097, 18119, 18121, 18127, 18131, 18133, 18143, 18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223, 18229, 18233, 18251, 18253, 18257, 18269, 18287, 18289, 18301, 18307,18311, 18313, 18329, 18341, 18353, 18367, 18371, 18379, 18397, 18401, 18413, 18427, 18433, 18439, 18443, 18451, 18457, 18461, 18481, 18493, 18503, 18517, 18521, 18523, 18539, 18541, 18553, 18583, 18587, 18593, 18617, 18637, 18661, 18671, 18679, 18691, 18701, 18713, 18719, 18731, 18743, 18749, 18757, 18773, 18787, 18793, 18797, 18803, 18839, 18859, 18869, 18899, 18911, 18913, 18917, 18919, 18947, 18959, 18973, 18979, 19001, 19009, 19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081, 19087, 19121, 19139, 19141, 19157, 19163, 19181, 19183, 19207, 19211, 19213, 19219, 19231, 19237, 19249, 19259, 19267, 19273, 19289, 19301, 19309, 19319, 19333, 19373, 19379, 19381, 19387, 19391, 19403, 19417, 19421, 19423, 19427, 19429, 19433, 19441, 19447, 19457, 19463, 19469, 19471, 19477, 19483, 19489, 19501, 19507, 19531, 19541, 19543, 19553, 19559, 19571, 19577, 19583, 19597, 19603, 19609, 19661, 19681, 19687, 19697, 19699, 19709, 19717, 19727, 19739, 19751, 19753, 19759, 19763, 19777, 19793, 19801, 19813, 19819, 19841, 19843, 19853, 19861,19867, 19889, 19891, 19913, 19919, 19927, 19937, 19949, 19961, 19963, 19973, 19979, 19991, 19993, 19997, 20011, 20021, 20023, 20029, 20047, 20051, 20063, 20071, 20089, 20101, 20107, 20113, 20117, 20123, 20129, 20143, 20147, 20149, 20161, 20173, 20177, 20183, 20201, 20219, 20231, 20233, 20249, 20261, 20269, 20287, 20297, 20323, 20327, 20333, 20341, 20347, 20353, 20357, 20359, 20369, 20389, 20393, 20399, 20407, 20411, 20431, 20441, 20443, 20477, 20479, 20483, 20507, 20509, 20521, 20533, 20543, 20549, 20551, 20563, 20593, 20599, 20611, 20627, 20639, 20641, 20663, 20681, 20693, 20707, 20717, 20719, 20731, 20743, 20747, 20749, 20753, 20759, 20771, 20773, 20789, 20807, 20809, 20849, 20857, 20873, 20879, 20887, 20897, 20899, 20903, 20921, 20929, 20939, 20947, 20959, 20963, 20981, 20983, 21001, 21011, 21013, 21017, 21019, 21023, 21031, 21059, 21061, 21067, 21089, 21101, 21107, 21121, 21139, 21143, 21149, 21157, 21163, 21169, 21179, 21187, 21191, 21193, 21211, 21221, 21227, 21247, 21269, 21277, 21283, 21313, 21317, 21319, 21323, 21341,21347, 21377, 21379, 21383, 21391, 21397, 21401, 21407, 21419, 21433, 21467, 21481, 21487, 21491, 21493, 21499, 21503, 21517, 21521, 21523, 21529, 21557, 21559, 21563, 21569, 21577, 21587, 21589, 21599, 21601, 21611, 21613, 21617, 21647, 21649, 21661, 21673, 21683, 21701, 21713, 21727, 21737, 21739, 21751, 21757, 21767, 21773, 21787, 21799, 21803, 21817, 21821, 21839, 21841, 21851, 21859, 21863, 21871, 21881, 21893, 21911, 21929, 21937, 21943, 21961, 21977, 21991, 21997, 22003, 22013, 22027, 22031, 22037, 22039, 22051, 22063, 22067, 22073, 22079, 22091, 22093, 22109, 22111, 22123, 22129, 22133, 22147, 22153, 22157, 22159, 22171, 22189, 22193, 22229, 22247, 22259, 22271, 22273, 22277, 22279, 22283, 22291, 22303, 22307, 22343, 22349, 22367, 22369, 22381, 22391, 22397, 22409, 22433, 22441, 22447, 22453, 22469, 22481, 22483, 22501, 22511, 22531, 22541, 22543, 22549, 22567, 22571, 22573, 22613, 22619, 22621, 22637, 22639, 22643, 22651, 22669, 22679, 22691, 22697, 22699, 22709, 22717, 22721, 22727, 22739, 22741, 22751, 22769, 22777,22783, 22787, 22807, 22811, 22817, 22853, 22859, 22861, 22871, 22877, 22901, 22907, 22921, 22937, 22943, 22961, 22963, 22973, 22993, 23003, 23011, 23017, 23021, 23027, 23029, 23039, 23041, 23053, 23057, 23059, 23063, 23071, 23081, 23087, 23099, 23117, 23131, 23143, 23159, 23167, 23173, 23189, 23197, 23201, 23203, 23209, 23227, 23251, 23269, 23279, 23291, 23293, 23297, 23311, 23321, 23327, 23333, 23339, 23357, 23369, 23371, 23399, 23417, 23431, 23447, 23459, 23473, 23497, 23509, 23531, 23537, 23539, 23549, 23557, 23561, 23563, 23567, 23581, 23593, 23599, 23603, 23609, 23623, 23627, 23629, 23633, 23663, 23669, 23671, 23677, 23687, 23689, 23719, 23741, 23743, 23747, 23753, 23761, 23767, 23773, 23789, 23801, 23813, 23819, 23827, 23831, 23833, 23857, 23869, 23873, 23879, 23887, 23893, 23899, 23909, 23911, 23917, 23929, 23957, 23971, 23977, 23981, 23993, 24001, 24007, 24019, 24023, 24029, 24043, 24049, 24061, 24071, 24077, 24083, 24091, 24097, 24103, 24107, 24109, 24113, 24121, 24133, 24137, 24151, 24169, 24179, 24181, 24197, 24203,24223, 24229, 24239, 24247, 24251, 24281, 24317, 24329, 24337, 24359, 24371, 24373, 24379, 24391, 24407, 24413, 24419, 24421, 24439, 24443, 24469, 24473, 24481, 24499, 24509, 24517, 24527, 24533, 24547, 24551, 24571, 24593, 24611, 24623, 24631, 24659, 24671, 24677, 24683, 24691, 24697, 24709, 24733, 24749, 24763, 24767, 24781, 24793, 24799, 24809, 24821, 24841, 24847, 24851, 24859, 24877, 24889, 24907, 24917, 24919, 24923, 24943, 24953, 24967, 24971, 24977, 24979, 24989, 25013, 25031, 25033, 25037, 25057, 25073, 25087, 25097, 25111, 25117, 25121, 25127, 25147, 25153, 25163, 25169, 25171, 25183, 25189, 25219, 25229, 25237, 25243, 25247, 25253, 25261, 25301, 25303, 25307, 25309, 25321, 25339, 25343, 25349, 25357, 25367, 25373, 25391, 25409, 25411, 25423, 25439, 25447, 25453, 25457, 25463, 25469, 25471, 25523, 25537, 25541, 25561, 25577, 25579, 25583, 25589, 25601, 25603, 25609, 25621, 25633, 25639, 25643, 25657, 25667, 25673, 25679, 25693, 25703, 25717, 25733, 25741, 25747, 25759, 25763, 25771, 25793, 25799, 25801, 25819, 25841,25847, 25849, 25867, 25873, 25889, 25903, 25913, 25919, 25931, 25933, 25939, 25943, 25951, 25969, 25981, 25997, 25999, 26003, 26017, 26021, 26029, 26041, 26053, 26083, 26099, 26107, 26111, 26113, 26119, 26141, 26153, 26161, 26171, 26177, 26183, 26189, 26203, 26209, 26227, 26237, 26249, 26251, 26261, 26263, 26267, 26293, 26297, 26309, 26317, 26321, 26339, 26347, 26357, 26371, 26387, 26393, 26399, 26407, 26417, 26423, 26431, 26437, 26449, 26459, 26479, 26489, 26497, 26501, 26513, 26539, 26557, 26561, 26573, 26591, 26597, 26627, 26633, 26641, 26647, 26669, 26681, 26683, 26687, 26693, 26699, 26701, 26711, 26713, 26717, 26723, 26729, 26731, 26737, 26759, 26777, 26783, 26801, 26813, 26821, 26833, 26839, 26849, 26861, 26863, 26879, 26881, 26891, 26893, 26903, 26921, 26927, 26947, 26951, 26953, 26959, 26981, 26987, 26993, 27011, 27017, 27031, 27043, 27059, 27061, 27067, 27073, 27077, 27091, 27103, 27107, 27109, 27127, 27143, 27179, 27191, 27197, 27211, 27239, 27241, 27253, 27259, 27271, 27277, 27281, 27283, 27299, 27329, 27337, 27361,27367, 27397, 27407, 27409, 27427, 27431, 27437, 27449, 27457, 27479, 27481, 27487, 27509, 27527, 27529, 27539, 27541, 27551, 27581, 27583, 27611, 27617, 27631, 27647, 27653, 27673, 27689, 27691, 27697, 27701, 27733, 27737, 27739, 27743, 27749, 27751, 27763, 27767, 27773, 27779, 27791, 27793, 27799, 27803, 27809, 27817, 27823, 27827, 27847, 27851, 27883, 27893, 27901, 27917, 27919, 27941, 27943, 27947, 27953, 27961, 27967, 27983, 27997, 28001, 28019, 28027, 28031, 28051, 28057, 28069, 28081, 28087, 28097, 28099, 28109, 28111, 28123, 28151, 28163, 28181, 28183, 28201, 28211, 28219, 28229, 28277, 28279, 28283, 28289, 28297, 28307, 28309, 28319, 28349, 28351, 28387, 28393, 28403, 28409, 28411, 28429, 28433, 28439, 28447, 28463, 28477, 28493, 28499, 28513, 28517, 28537, 28541, 28547, 28549, 28559, 28571, 28573, 28579, 28591, 28597, 28603, 28607, 28619, 28621, 28627, 28631, 28643, 28649, 28657, 28661, 28663, 28669, 28687, 28697, 28703, 28711, 28723, 28729, 28751, 28753, 28759, 28771, 28789, 28793, 28807, 28813, 28817, 28837, 28843,28859, 28867, 28871, 28879, 28901, 28909, 28921, 28927, 28933, 28949, 28961, 28979, 29009, 29017, 29021, 29023, 29027, 29033, 29059, 29063, 29077, 29101, 29123, 29129, 29131, 29137, 29147, 29153, 29167, 29173, 29179, 29191, 29201, 29207, 29209, 29221, 29231, 29243, 29251, 29269, 29287, 29297, 29303, 29311, 29327, 29333, 29339, 29347, 29363, 29383, 29387, 29389, 29399, 29401, 29411, 29423, 29429, 29437, 29443, 29453, 29473, 29483, 29501, 29527, 29531, 29537, 29567, 29569, 29573, 29581, 29587, 29599, 29611, 29629, 29633, 29641, 29663, 29669, 29671, 29683, 29717, 29723, 29741, 29753, 29759, 29761, 29789, 29803, 29819, 29833, 29837, 29851, 29863, 29867, 29873, 29879, 29881, 29917, 29921, 29927, 29947, 29959, 29983, 29989, 30011, 30013, 30029, 30047, 30059, 30071, 30089, 30091, 30097, 30103, 30109, 30113, 30119, 30133, 30137, 30139, 30161, 30169, 30181, 30187, 30197, 30203, 30211, 30223, 30241, 30253, 30259, 30269, 30271, 30293, 30307, 30313, 30319, 30323, 30341, 30347, 30367, 30389, 30391, 30403, 30427, 30431, 30449, 30467, 30469,30491, 30493, 30497, 30509, 30517, 30529, 30539, 30553, 30557, 30559, 30577, 30593, 30631, 30637, 30643, 30649, 30661, 30671, 30677, 30689, 30697, 30703, 30707, 30713, 30727, 30757, 30763, 30773, 30781, 30803, 30809, 30817, 30829, 30839, 30841, 30851, 30853, 30859, 30869, 30871, 30881, 30893, 30911, 30931, 30937, 30941, 30949, 30971, 30977, 30983, 31013, 31019, 31033, 31039, 31051, 31063, 31069, 31079, 31081, 31091, 31121, 31123, 31139, 31147, 31151, 31153, 31159, 31177, 31181, 31183, 31189, 31193, 31219, 31223, 31231, 31237, 31247, 31249, 31253, 31259, 31267, 31271, 31277, 31307, 31319, 31321, 31327, 31333, 31337, 31357, 31379, 31387, 31391, 31393, 31397, 31469, 31477, 31481, 31489, 31511, 31513, 31517, 31531, 31541, 31543, 31547, 31567, 31573, 31583, 31601, 31607, 31627, 31643, 31649, 31657, 31663, 31667, 31687, 31699, 31721, 31723, 31727, 31729, 31741, 31751, 31769, 31771, 31793, 31799, 31817, 31847, 31849, 31859, 31873, 31883, 31891, 31907, 31957, 31963, 31973, 31981, 31991, 32003, 32009, 32027, 32029, 32051, 32057, 32059,32063, 32069, 32077, 32083, 32089, 32099, 32117, 32119, 32141, 32143, 32159, 32173, 32183, 32189, 32191, 32203, 32213, 32233, 32237, 32251, 32257, 32261, 32297, 32299, 32303, 32309, 32321, 32323, 32327, 32341, 32353, 32359, 32363, 32369, 32371, 32377, 32381, 32401, 32411, 32413, 32423, 32429, 32441, 32443, 32467, 32479, 32491, 32497, 32503, 32507, 32531, 32533, 32537, 32561, 32563, 32569, 32573, 32579, 32587, 32603, 32609, 32611, 32621, 32633, 32647, 32653, 32687, 32693, 32707, 32713, 32717, 32719, 32749, 32771, 32779, 32783, 32789, 32797, 32801, 32803, 32831, 32833, 32839, 32843, 32869, 32887, 32909, 32911, 32917, 32933, 32939, 32941, 32957, 32969, 32971, 32983, 32987, 32993, 32999, 33013, 33023, 33029, 33037, 33049, 33053, 33071, 33073, 33083, 33091, 33107, 33113, 33119, 33149, 33151, 33161, 33179, 33181, 33191, 33199, 33203, 33211, 33223, 33247, 33287, 33289, 33301, 33311, 33317, 33329, 33331, 33343, 33347, 33349, 33353, 33359, 33377, 33391, 33403, 33409, 33413, 33427, 33457, 33461, 33469, 33479, 33487, 33493, 33503, 33521,33529, 33533, 33547, 33563, 33569, 33577, 33581, 33587, 33589, 33599, 33601, 33613, 33617, 33619, 33623, 33629, 33637, 33641, 33647, 33679, 33703, 33713, 33721, 33739, 33749, 33751, 33757, 33767, 33769, 33773, 33791, 33797, 33809, 33811, 33827, 33829, 33851, 33857, 33863, 33871, 33889, 33893, 33911, 33923, 33931, 33937, 33941, 33961, 33967, 33997, 34019, 34031, 34033, 34039, 34057, 34061, 34123, 34127, 34129, 34141, 34147, 34157, 34159, 34171, 34183, 34211, 34213, 34217, 34231, 34253, 34259, 34261, 34267, 34273, 34283, 34297, 34301, 34303, 34313, 34319, 34327, 34337, 34351, 34361, 34367, 34369, 34381, 34403, 34421, 34429, 34439, 34457, 34469, 34471, 34483, 34487, 34499, 34501, 34511, 34513, 34519, 34537, 34543, 34549, 34583, 34589, 34591, 34603, 34607, 34613, 34631, 34649, 34651, 34667, 34673, 34679, 34687, 34693, 34703, 34721, 34729, 34739, 34747, 34757, 34759, 34763, 34781, 34807, 34819, 34841, 34843, 34847, 34849, 34871, 34877, 34883, 34897, 34913, 34919, 34939, 34949, 34961, 34963, 34981, 35023, 35027, 35051, 35053, 35059,35069, 35081, 35083, 35089, 35099, 35107, 35111, 35117, 35129, 35141, 35149, 35153, 35159, 35171, 35201, 35221, 35227, 35251, 35257, 35267, 35279, 35281, 35291, 35311, 35317, 35323, 35327, 35339, 35353, 35363, 35381, 35393, 35401, 35407, 35419, 35423, 35437, 35447, 35449, 35461, 35491, 35507, 35509, 35521, 35527, 35531, 35533, 35537, 35543, 35569, 35573, 35591, 35593, 35597, 35603, 35617, 35671, 35677, 35729, 35731, 35747, 35753, 35759, 35771, 35797, 35801, 35803, 35809, 35831, 35837, 35839, 35851, 35863, 35869, 35879, 35897, 35899, 35911, 35923, 35933, 35951, 35963, 35969, 35977, 35983, 35993, 35999, 36007, 36011, 36013, 36017, 36037, 36061, 36067, 36073, 36083, 36097, 36107, 36109, 36131, 36137, 36151, 36161, 36187, 36191, 36209, 36217, 36229, 36241, 36251, 36263, 36269, 36277, 36293, 36299, 36307, 36313, 36319, 36341, 36343, 36353, 36373, 36383, 36389, 36433, 36451, 36457, 36467, 36469, 36473, 36479, 36493, 36497, 36523, 36527, 36529, 36541, 36551, 36559, 36563, 36571, 36583, 36587, 36599, 36607, 36629, 36637, 36643, 36653,36671, 36677, 36683, 36691, 36697, 36709, 36713, 36721, 36739, 36749, 36761, 36767, 36779, 36781, 36787, 36791, 36793, 36809, 36821, 36833, 36847, 36857, 36871, 36877, 36887, 36899, 36901, 36913, 36919, 36923, 36929, 36931, 36943, 36947, 36973, 36979, 36997, 37003, 37013, 37019, 37021, 37039, 37049, 37057, 37061, 37087, 37097, 37117, 37123, 37139, 37159, 37171, 37181, 37189, 37199, 37201, 37217, 37223, 37243, 37253, 37273, 37277, 37307, 37309, 37313, 37321, 37337, 37339, 37357, 37361, 37363, 37369, 37379, 37397, 37409, 37423, 37441, 37447, 37463, 37483, 37489, 37493, 37501, 37507, 37511, 37517, 37529, 37537, 37547, 37549, 37561, 37567, 37571, 37573, 37579, 37589, 37591, 37607, 37619, 37633, 37643, 37649, 37657, 37663, 37691, 37693, 37699, 37717, 37747, 37781, 37783, 37799, 37811, 37813, 37831, 37847, 37853, 37861, 37871, 37879, 37889, 37897, 37907, 37951, 37957, 37963, 37967, 37987, 37991, 37993, 37997, 38011, 38039, 38047, 38053, 38069, 38083, 38113, 38119, 38149, 38153, 38167, 38177, 38183, 38189, 38197, 38201, 38219, 38231,38237, 38239, 38261, 38273, 38281, 38287, 38299, 38303, 38317, 38321, 38327, 38329, 38333, 38351, 38371, 38377, 38393, 38431, 38447, 38449, 38453, 38459, 38461, 38501, 38543, 38557, 38561, 38567, 38569, 38593, 38603, 38609, 38611, 38629, 38639, 38651, 38653, 38669, 38671, 38677, 38693, 38699, 38707, 38711, 38713, 38723, 38729, 38737, 38747, 38749, 38767, 38783, 38791, 38803, 38821, 38833, 38839, 38851, 38861, 38867, 38873, 38891, 38903, 38917, 38921, 38923, 38933, 38953, 38959, 38971, 38977, 38993, 39019, 39023, 39041, 39043, 39047, 39079, 39089, 39097, 39103, 39107, 39113, 39119, 39133, 39139, 39157, 39161, 39163, 39181, 39191, 39199, 39209, 39217, 39227, 39229, 39233, 39239, 39241, 39251, 39293, 39301, 39313, 39317, 39323, 39341, 39343, 39359, 39367, 39371, 39373, 39383, 39397, 39409, 39419, 39439, 39443, 39451, 39461, 39499, 39503, 39509, 39511, 39521, 39541, 39551, 39563, 39569, 39581, 39607, 39619, 39623, 39631, 39659, 39667, 39671, 39679, 39703, 39709, 39719, 39727, 39733, 39749, 39761, 39769, 39779, 39791, 39799, 39821,39827, 39829, 39839, 39841, 39847, 39857, 39863, 39869, 39877, 39883, 39887, 39901, 39929, 39937, 39953, 39971, 39979, 39983, 39989, 40009, 40013, 40031, 40037, 40039, 40063, 40087, 40093, 40099, 40111, 40123, 40127, 40129, 40151, 40153, 40163, 40169, 40177, 40189, 40193, 40213, 40231, 40237, 40241, 40253, 40277, 40283, 40289, 40343, 40351, 40357, 40361, 40387, 40423, 40427, 40429, 40433, 40459, 40471, 40483, 40487, 40493, 40499, 40507, 40519, 40529, 40531, 40543, 40559, 40577, 40583, 40591, 40597, 40609, 40627, 40637, 40639, 40693, 40697, 40699, 40709, 40739, 40751, 40759, 40763, 40771, 40787, 40801, 40813, 40819, 40823, 40829, 40841, 40847, 40849, 40853, 40867, 40879, 40883, 40897, 40903, 40927, 40933, 40939, 40949, 40961, 40973, 40993, 41011, 41017, 41023, 41039, 41047, 41051, 41057, 41077, 41081, 41113, 41117, 41131, 41141, 41143, 41149, 41161, 41177, 41179, 41183, 41189, 41201, 41203, 41213, 41221, 41227, 41231, 41233, 41243, 41257, 41263, 41269, 41281, 41299, 41333, 41341, 41351, 41357, 41381, 41387, 41389, 41399, 41411,41413, 41443, 41453, 41467, 41479, 41491, 41507, 41513, 41519, 41521, 41539, 41543, 41549, 41579, 41593, 41597, 41603, 41609, 41611, 41617, 41621]
X = []
for p in prime:
cnt = 0
while M%p==0:
M//=p
cnt += 1
if cnt>0:
X.append(cnt)
if M!=1:
X.append(M)
Ans = 1
for x in X:
for i in range(1,x+1):
Ans = ((Ans * (N+x-i)) //i)
print((Ans % 1000000007))
| N,M = list(map(int,input().split()))
prime = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499,503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823,1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229,4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507,5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823,6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171,8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479,9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171,11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577,12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, 13997,13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401,15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569, 15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661, 15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, 16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, 16427, 16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, 16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889, 16901,16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, 16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, 17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, 17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 17321, 17327, 17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519, 17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599, 17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737, 17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863, 17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939, 17957, 17959, 17971, 17977, 17981, 17987, 17989, 18013, 18041, 18043, 18047, 18049, 18059, 18061, 18077, 18089, 18097, 18119, 18121, 18127, 18131, 18133, 18143, 18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223, 18229, 18233, 18251, 18253, 18257, 18269, 18287, 18289, 18301, 18307,18311, 18313, 18329, 18341, 18353, 18367, 18371, 18379, 18397, 18401, 18413, 18427, 18433, 18439, 18443, 18451, 18457, 18461, 18481, 18493, 18503, 18517, 18521, 18523, 18539, 18541, 18553, 18583, 18587, 18593, 18617, 18637, 18661, 18671, 18679, 18691, 18701, 18713, 18719, 18731, 18743, 18749, 18757, 18773, 18787, 18793, 18797, 18803, 18839, 18859, 18869, 18899, 18911, 18913, 18917, 18919, 18947, 18959, 18973, 18979, 19001, 19009, 19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081, 19087, 19121, 19139, 19141, 19157, 19163, 19181, 19183, 19207, 19211, 19213, 19219, 19231, 19237, 19249, 19259, 19267, 19273, 19289, 19301, 19309, 19319, 19333, 19373, 19379, 19381, 19387, 19391, 19403, 19417, 19421, 19423, 19427, 19429, 19433, 19441, 19447, 19457, 19463, 19469, 19471, 19477, 19483, 19489, 19501, 19507, 19531, 19541, 19543, 19553, 19559, 19571, 19577, 19583, 19597, 19603, 19609, 19661, 19681, 19687, 19697, 19699, 19709, 19717, 19727, 19739, 19751, 19753, 19759, 19763, 19777, 19793, 19801, 19813, 19819, 19841, 19843, 19853, 19861,19867, 19889, 19891, 19913, 19919, 19927, 19937, 19949, 19961, 19963, 19973, 19979, 19991, 19993, 19997, 20011, 20021, 20023, 20029, 20047, 20051, 20063, 20071, 20089, 20101, 20107, 20113, 20117, 20123, 20129, 20143, 20147, 20149, 20161, 20173, 20177, 20183, 20201, 20219, 20231, 20233, 20249, 20261, 20269, 20287, 20297, 20323, 20327, 20333, 20341, 20347, 20353, 20357, 20359, 20369, 20389, 20393, 20399, 20407, 20411, 20431, 20441, 20443, 20477, 20479, 20483, 20507, 20509, 20521, 20533, 20543, 20549, 20551, 20563, 20593, 20599, 20611, 20627, 20639, 20641, 20663, 20681, 20693, 20707, 20717, 20719, 20731, 20743, 20747, 20749, 20753, 20759, 20771, 20773, 20789, 20807, 20809, 20849, 20857, 20873, 20879, 20887, 20897, 20899, 20903, 20921, 20929, 20939, 20947, 20959, 20963, 20981, 20983, 21001, 21011, 21013, 21017, 21019, 21023, 21031, 21059, 21061, 21067, 21089, 21101, 21107, 21121, 21139, 21143, 21149, 21157, 21163, 21169, 21179, 21187, 21191, 21193, 21211, 21221, 21227, 21247, 21269, 21277, 21283, 21313, 21317, 21319, 21323, 21341,21347, 21377, 21379, 21383, 21391, 21397, 21401, 21407, 21419, 21433, 21467, 21481, 21487, 21491, 21493, 21499, 21503, 21517, 21521, 21523, 21529, 21557, 21559, 21563, 21569, 21577, 21587, 21589, 21599, 21601, 21611, 21613, 21617, 21647, 21649, 21661, 21673, 21683, 21701, 21713, 21727, 21737, 21739, 21751, 21757, 21767, 21773, 21787, 21799, 21803, 21817, 21821, 21839, 21841, 21851, 21859, 21863, 21871, 21881, 21893, 21911, 21929, 21937, 21943, 21961, 21977, 21991, 21997, 22003, 22013, 22027, 22031, 22037, 22039, 22051, 22063, 22067, 22073, 22079, 22091, 22093, 22109, 22111, 22123, 22129, 22133, 22147, 22153, 22157, 22159, 22171, 22189, 22193, 22229, 22247, 22259, 22271, 22273, 22277, 22279, 22283, 22291, 22303, 22307, 22343, 22349, 22367, 22369, 22381, 22391, 22397, 22409, 22433, 22441, 22447, 22453, 22469, 22481, 22483, 22501, 22511, 22531, 22541, 22543, 22549, 22567, 22571, 22573, 22613, 22619, 22621, 22637, 22639, 22643, 22651, 22669, 22679, 22691, 22697, 22699, 22709, 22717, 22721, 22727, 22739, 22741, 22751, 22769, 22777,22783, 22787, 22807, 22811, 22817, 22853, 22859, 22861, 22871, 22877, 22901, 22907, 22921, 22937, 22943, 22961, 22963, 22973, 22993, 23003, 23011, 23017, 23021, 23027, 23029, 23039, 23041, 23053, 23057, 23059, 23063, 23071, 23081, 23087, 23099, 23117, 23131, 23143, 23159, 23167, 23173, 23189, 23197, 23201, 23203, 23209, 23227, 23251, 23269, 23279, 23291, 23293, 23297, 23311, 23321, 23327, 23333, 23339, 23357, 23369, 23371, 23399, 23417, 23431, 23447, 23459, 23473, 23497, 23509, 23531, 23537, 23539, 23549, 23557, 23561, 23563, 23567, 23581, 23593, 23599, 23603, 23609, 23623, 23627, 23629, 23633, 23663, 23669, 23671, 23677, 23687, 23689, 23719, 23741, 23743, 23747, 23753, 23761, 23767, 23773, 23789, 23801, 23813, 23819, 23827, 23831, 23833, 23857, 23869, 23873, 23879, 23887, 23893, 23899, 23909, 23911, 23917, 23929, 23957, 23971, 23977, 23981, 23993, 24001, 24007, 24019, 24023, 24029, 24043, 24049, 24061, 24071, 24077, 24083, 24091, 24097, 24103, 24107, 24109, 24113, 24121, 24133, 24137, 24151, 24169, 24179, 24181, 24197, 24203,24223, 24229, 24239, 24247, 24251, 24281, 24317, 24329, 24337, 24359, 24371, 24373, 24379, 24391, 24407, 24413, 24419, 24421, 24439, 24443, 24469, 24473, 24481, 24499, 24509, 24517, 24527, 24533, 24547, 24551, 24571, 24593, 24611, 24623, 24631, 24659, 24671, 24677, 24683, 24691, 24697, 24709, 24733, 24749, 24763, 24767, 24781, 24793, 24799, 24809, 24821, 24841, 24847, 24851, 24859, 24877, 24889, 24907, 24917, 24919, 24923, 24943, 24953, 24967, 24971, 24977, 24979, 24989, 25013, 25031, 25033, 25037, 25057, 25073, 25087, 25097, 25111, 25117, 25121, 25127, 25147, 25153, 25163, 25169, 25171, 25183, 25189, 25219, 25229, 25237, 25243, 25247, 25253, 25261, 25301, 25303, 25307, 25309, 25321, 25339, 25343, 25349, 25357, 25367, 25373, 25391, 25409, 25411, 25423, 25439, 25447, 25453, 25457, 25463, 25469, 25471, 25523, 25537, 25541, 25561, 25577, 25579, 25583, 25589, 25601, 25603, 25609, 25621, 25633, 25639, 25643, 25657, 25667, 25673, 25679, 25693, 25703, 25717, 25733, 25741, 25747, 25759, 25763, 25771, 25793, 25799, 25801, 25819, 25841,25847, 25849, 25867, 25873, 25889, 25903, 25913, 25919, 25931, 25933, 25939, 25943, 25951, 25969, 25981, 25997, 25999, 26003, 26017, 26021, 26029, 26041, 26053, 26083, 26099, 26107, 26111, 26113, 26119, 26141, 26153, 26161, 26171, 26177, 26183, 26189, 26203, 26209, 26227, 26237, 26249, 26251, 26261, 26263, 26267, 26293, 26297, 26309, 26317, 26321, 26339, 26347, 26357, 26371, 26387, 26393, 26399, 26407, 26417, 26423, 26431, 26437, 26449, 26459, 26479, 26489, 26497, 26501, 26513, 26539, 26557, 26561, 26573, 26591, 26597, 26627, 26633, 26641, 26647, 26669, 26681, 26683, 26687, 26693, 26699, 26701, 26711, 26713, 26717, 26723, 26729, 26731, 26737, 26759, 26777, 26783, 26801, 26813, 26821, 26833, 26839, 26849, 26861, 26863, 26879, 26881, 26891, 26893, 26903, 26921, 26927, 26947, 26951, 26953, 26959, 26981, 26987, 26993, 27011, 27017, 27031, 27043, 27059, 27061, 27067, 27073, 27077, 27091, 27103, 27107, 27109, 27127, 27143, 27179, 27191, 27197, 27211, 27239, 27241, 27253, 27259, 27271, 27277, 27281, 27283, 27299, 27329, 27337, 27361,27367, 27397, 27407, 27409, 27427, 27431, 27437, 27449, 27457, 27479, 27481, 27487, 27509, 27527, 27529, 27539, 27541, 27551, 27581, 27583, 27611, 27617, 27631, 27647, 27653, 27673, 27689, 27691, 27697, 27701, 27733, 27737, 27739, 27743, 27749, 27751, 27763, 27767, 27773, 27779, 27791, 27793, 27799, 27803, 27809, 27817, 27823, 27827, 27847, 27851, 27883, 27893, 27901, 27917, 27919, 27941, 27943, 27947, 27953, 27961, 27967, 27983, 27997, 28001, 28019, 28027, 28031, 28051, 28057, 28069, 28081, 28087, 28097, 28099, 28109, 28111, 28123, 28151, 28163, 28181, 28183, 28201, 28211, 28219, 28229, 28277, 28279, 28283, 28289, 28297, 28307, 28309, 28319, 28349, 28351, 28387, 28393, 28403, 28409, 28411, 28429, 28433, 28439, 28447, 28463, 28477, 28493, 28499, 28513, 28517, 28537, 28541, 28547, 28549, 28559, 28571, 28573, 28579, 28591, 28597, 28603, 28607, 28619, 28621, 28627, 28631, 28643, 28649, 28657, 28661, 28663, 28669, 28687, 28697, 28703, 28711, 28723, 28729, 28751, 28753, 28759, 28771, 28789, 28793, 28807, 28813, 28817, 28837, 28843,28859, 28867, 28871, 28879, 28901, 28909, 28921, 28927, 28933, 28949, 28961, 28979, 29009, 29017, 29021, 29023, 29027, 29033, 29059, 29063, 29077, 29101, 29123, 29129, 29131, 29137, 29147, 29153, 29167, 29173, 29179, 29191, 29201, 29207, 29209, 29221, 29231, 29243, 29251, 29269, 29287, 29297, 29303, 29311, 29327, 29333, 29339, 29347, 29363, 29383, 29387, 29389, 29399, 29401, 29411, 29423, 29429, 29437, 29443, 29453, 29473, 29483, 29501, 29527, 29531, 29537, 29567, 29569, 29573, 29581, 29587, 29599, 29611, 29629, 29633, 29641, 29663, 29669, 29671, 29683, 29717, 29723, 29741, 29753, 29759, 29761, 29789, 29803, 29819, 29833, 29837, 29851, 29863, 29867, 29873, 29879, 29881, 29917, 29921, 29927, 29947, 29959, 29983, 29989, 30011, 30013, 30029, 30047, 30059, 30071, 30089, 30091, 30097, 30103, 30109, 30113, 30119, 30133, 30137, 30139, 30161, 30169, 30181, 30187, 30197, 30203, 30211, 30223, 30241, 30253, 30259, 30269, 30271, 30293, 30307, 30313, 30319, 30323, 30341, 30347, 30367, 30389, 30391, 30403, 30427, 30431, 30449, 30467, 30469,30491, 30493, 30497, 30509, 30517, 30529, 30539, 30553, 30557, 30559, 30577, 30593, 30631, 30637, 30643, 30649, 30661, 30671, 30677, 30689, 30697, 30703, 30707, 30713, 30727, 30757, 30763, 30773, 30781, 30803, 30809, 30817, 30829, 30839, 30841, 30851, 30853, 30859, 30869, 30871, 30881, 30893, 30911, 30931, 30937, 30941, 30949, 30971, 30977, 30983, 31013, 31019, 31033, 31039, 31051, 31063, 31069, 31079, 31081, 31091, 31121, 31123, 31139, 31147, 31151, 31153, 31159, 31177, 31181, 31183, 31189, 31193, 31219, 31223, 31231, 31237, 31247, 31249, 31253, 31259, 31267, 31271, 31277, 31307, 31319, 31321, 31327, 31333, 31337, 31357, 31379, 31387, 31391, 31393, 31397, 31469, 31477, 31481, 31489, 31511, 31513, 31517, 31531, 31541, 31543, 31547, 31567, 31573, 31583, 31601, 31607, 31627, 31643, 31649, 31657, 31663, 31667, 31687, 31699, 31721, 31723, 31727, 31729, 31741, 31751, 31769, 31771, 31793, 31799, 31817, 31847, 31849, 31859, 31873, 31883, 31891, 31907, 31957, 31963, 31973, 31981, 31991, 32003, 32009, 32027, 32029, 32051, 32057, 32059,32063, 32069, 32077, 32083, 32089, 32099, 32117, 32119, 32141, 32143, 32159, 32173, 32183, 32189, 32191, 32203, 32213, 32233, 32237, 32251, 32257, 32261, 32297, 32299, 32303, 32309, 32321, 32323, 32327, 32341, 32353, 32359, 32363, 32369, 32371, 32377, 32381, 32401, 32411, 32413, 32423, 32429, 32441, 32443, 32467, 32479, 32491, 32497, 32503, 32507, 32531, 32533, 32537, 32561, 32563, 32569, 32573, 32579, 32587, 32603, 32609, 32611, 32621, 32633, 32647, 32653, 32687, 32693, 32707, 32713, 32717, 32719, 32749, 32771, 32779, 32783, 32789, 32797, 32801, 32803, 32831, 32833, 32839, 32843, 32869, 32887, 32909, 32911, 32917, 32933, 32939, 32941, 32957, 32969, 32971, 32983, 32987, 32993, 32999, 33013, 33023, 33029, 33037, 33049, 33053, 33071, 33073, 33083, 33091, 33107, 33113, 33119, 33149, 33151, 33161, 33179, 33181, 33191, 33199, 33203, 33211, 33223, 33247, 33287, 33289, 33301, 33311, 33317, 33329, 33331, 33343, 33347, 33349, 33353, 33359, 33377, 33391, 33403, 33409, 33413, 33427, 33457, 33461, 33469, 33479, 33487, 33493, 33503, 33521,33529, 33533, 33547, 33563, 33569, 33577, 33581, 33587, 33589, 33599, 33601, 33613, 33617, 33619, 33623, 33629, 33637, 33641, 33647, 33679, 33703, 33713, 33721, 33739, 33749, 33751, 33757, 33767, 33769, 33773, 33791, 33797, 33809, 33811, 33827, 33829, 33851, 33857, 33863, 33871, 33889, 33893, 33911, 33923, 33931, 33937, 33941, 33961, 33967, 33997, 34019, 34031, 34033, 34039, 34057, 34061, 34123, 34127, 34129, 34141, 34147, 34157, 34159, 34171, 34183, 34211, 34213, 34217, 34231, 34253, 34259, 34261, 34267, 34273, 34283, 34297, 34301, 34303, 34313, 34319, 34327, 34337, 34351, 34361, 34367, 34369, 34381, 34403, 34421, 34429, 34439, 34457, 34469, 34471, 34483, 34487, 34499, 34501, 34511, 34513, 34519, 34537, 34543, 34549, 34583, 34589, 34591, 34603, 34607, 34613, 34631, 34649, 34651, 34667, 34673, 34679, 34687, 34693, 34703, 34721, 34729, 34739, 34747, 34757, 34759, 34763, 34781, 34807, 34819, 34841, 34843, 34847, 34849, 34871, 34877, 34883, 34897, 34913, 34919, 34939, 34949, 34961, 34963, 34981, 35023, 35027, 35051, 35053, 35059,35069, 35081, 35083, 35089, 35099, 35107, 35111, 35117, 35129, 35141, 35149, 35153, 35159, 35171, 35201, 35221, 35227, 35251, 35257, 35267, 35279, 35281, 35291, 35311, 35317, 35323, 35327, 35339, 35353, 35363, 35381, 35393, 35401, 35407, 35419, 35423, 35437, 35447, 35449, 35461, 35491, 35507, 35509, 35521, 35527, 35531, 35533, 35537, 35543, 35569, 35573, 35591, 35593, 35597, 35603, 35617, 35671, 35677, 35729, 35731, 35747, 35753, 35759, 35771, 35797, 35801, 35803, 35809, 35831, 35837, 35839, 35851, 35863, 35869, 35879, 35897, 35899, 35911, 35923, 35933, 35951, 35963, 35969, 35977, 35983, 35993, 35999, 36007, 36011, 36013, 36017, 36037, 36061, 36067, 36073, 36083, 36097, 36107, 36109, 36131, 36137, 36151, 36161, 36187, 36191, 36209, 36217, 36229, 36241, 36251, 36263, 36269, 36277, 36293, 36299, 36307, 36313, 36319, 36341, 36343, 36353, 36373, 36383, 36389, 36433, 36451, 36457, 36467, 36469, 36473, 36479, 36493, 36497, 36523, 36527, 36529, 36541, 36551, 36559, 36563, 36571, 36583, 36587, 36599, 36607, 36629, 36637, 36643, 36653,36671, 36677, 36683, 36691, 36697, 36709, 36713, 36721, 36739, 36749, 36761, 36767, 36779, 36781, 36787, 36791, 36793, 36809, 36821, 36833, 36847, 36857, 36871, 36877, 36887, 36899, 36901, 36913, 36919, 36923, 36929, 36931, 36943, 36947, 36973, 36979, 36997, 37003, 37013, 37019, 37021, 37039, 37049, 37057, 37061, 37087, 37097, 37117, 37123, 37139, 37159, 37171, 37181, 37189, 37199, 37201, 37217, 37223, 37243, 37253, 37273, 37277, 37307, 37309, 37313, 37321, 37337, 37339, 37357, 37361, 37363, 37369, 37379, 37397, 37409, 37423, 37441, 37447, 37463, 37483, 37489, 37493, 37501, 37507, 37511, 37517, 37529, 37537, 37547, 37549, 37561, 37567, 37571, 37573, 37579, 37589, 37591, 37607, 37619, 37633, 37643, 37649, 37657, 37663, 37691, 37693, 37699, 37717, 37747, 37781, 37783, 37799, 37811, 37813, 37831, 37847, 37853, 37861, 37871, 37879, 37889, 37897, 37907, 37951, 37957, 37963, 37967, 37987, 37991, 37993, 37997, 38011, 38039, 38047, 38053, 38069, 38083, 38113, 38119, 38149, 38153, 38167, 38177, 38183, 38189, 38197, 38201, 38219, 38231,38237, 38239, 38261, 38273, 38281, 38287, 38299, 38303, 38317, 38321, 38327, 38329, 38333, 38351, 38371, 38377, 38393, 38431, 38447, 38449, 38453, 38459, 38461, 38501, 38543, 38557, 38561, 38567, 38569, 38593, 38603, 38609, 38611, 38629, 38639, 38651, 38653, 38669, 38671, 38677, 38693, 38699, 38707, 38711, 38713, 38723, 38729, 38737, 38747, 38749, 38767, 38783, 38791, 38803, 38821, 38833, 38839, 38851, 38861, 38867, 38873, 38891, 38903, 38917, 38921, 38923, 38933, 38953, 38959, 38971, 38977, 38993, 39019, 39023, 39041, 39043, 39047, 39079, 39089, 39097, 39103, 39107, 39113, 39119, 39133, 39139, 39157, 39161, 39163, 39181, 39191, 39199, 39209, 39217, 39227, 39229, 39233, 39239, 39241, 39251, 39293, 39301, 39313, 39317, 39323, 39341, 39343, 39359, 39367, 39371, 39373, 39383, 39397, 39409, 39419, 39439, 39443, 39451, 39461, 39499, 39503, 39509, 39511, 39521, 39541, 39551, 39563, 39569, 39581, 39607, 39619, 39623, 39631, 39659, 39667, 39671, 39679, 39703, 39709, 39719, 39727, 39733, 39749, 39761, 39769, 39779, 39791, 39799, 39821,39827, 39829, 39839, 39841, 39847, 39857, 39863, 39869, 39877, 39883, 39887, 39901, 39929, 39937, 39953, 39971, 39979, 39983, 39989, 40009, 40013, 40031, 40037, 40039, 40063, 40087, 40093, 40099, 40111, 40123, 40127, 40129, 40151, 40153, 40163, 40169, 40177, 40189, 40193, 40213, 40231, 40237, 40241, 40253, 40277, 40283, 40289, 40343, 40351, 40357, 40361, 40387, 40423, 40427, 40429, 40433, 40459, 40471, 40483, 40487, 40493, 40499, 40507, 40519, 40529, 40531, 40543, 40559, 40577, 40583, 40591, 40597, 40609, 40627, 40637, 40639, 40693, 40697, 40699, 40709, 40739, 40751, 40759, 40763, 40771, 40787, 40801, 40813, 40819, 40823, 40829, 40841, 40847, 40849, 40853, 40867, 40879, 40883, 40897, 40903, 40927, 40933, 40939, 40949, 40961, 40973, 40993, 41011, 41017, 41023, 41039, 41047, 41051, 41057, 41077, 41081, 41113, 41117, 41131, 41141, 41143, 41149, 41161, 41177, 41179, 41183, 41189, 41201, 41203, 41213, 41221, 41227, 41231, 41233, 41243, 41257, 41263, 41269, 41281, 41299, 41333, 41341, 41351, 41357, 41381, 41387, 41389, 41399, 41411,41413, 41443, 41453, 41467, 41479, 41491, 41507, 41513, 41519, 41521, 41539, 41543, 41549, 41579, 41593, 41597, 41603, 41609, 41611, 41617, 41621]
X = []
for p in prime:
cnt = 0
while M%p==0:
M//=p
cnt += 1
if cnt>0:
X.append(cnt)
if M!=1:
X.append(1)
Ans = 1
for x in X:
for i in range(1,x+1):
Ans = ((Ans * (N+x-i)) //i)
print((Ans % 1000000007))
| p03253 |
from math import floor, sqrt
from collections import Counter
MOD = 10 ** 9 + 7
# xを素因数分解する
def getPrimeFactor(x):
ans = []
for d in range(2, floor(sqrt(x)) + 1):
while x % d == 0:
ans.append(d)
x //= d
if x != 1:
ans.append(x)
return ans
# xのn乗（二分累乗法）
def power(x, n):
ans = 1
while n:
if n % 2 == 1:
ans = (ans * x) % MOD
x = (x * x) % MOD
n //= 2
return ans
N, M = list(map(int, input().split()))
PFs = getPrimeFactor(M)
cnt = Counter(PFs)
N2 = N
if len(cnt):
N2 += max(cnt.values())
# facts[x]: xの階乗
facts = [1] + [0] * N2
for x in range(1, N2 + 1):
facts[x] = (facts[x - 1] * x) % MOD
# invFs[x]: xの階乗の逆元
invFs = [0] * N2 + [power(facts[N2], MOD - 2)]
for x in reversed(list(range(N2))):
invFs[x] = (invFs[x + 1] * (x + 1)) % MOD
def comb(n, k):
return ((facts[n] * invFs[k]) % MOD * invFs[n - k]) % MOD
ans = 1
for num in list(cnt.values()):
ans = (ans * comb(N + num - 1, num)) % MOD
print(ans)
| from math import floor, sqrt
from collections import Counter
MOD = 10 ** 9 + 7
# xを素因数分解する
def getPrimeFactor(x):
ans = []
for d in range(2, floor(sqrt(x)) + 1):
while x % d == 0:
ans.append(d)
x //= d
if x != 1:
ans.append(x)
return ans
def comb(n, k):
k = min(k, n - k)
ans = 1
for i in range(n, n - k, -1):
ans *= i
for i in range(1, k + 1):
ans //= i
return ans
N, M = list(map(int, input().split()))
PFs = getPrimeFactor(M)
cnt = Counter(PFs)
ans = 1
for num in list(cnt.values()):
ans *= comb(N + num - 1, num)
print((ans % MOD))
| p03253 |
def prime_facts(n: int) -> dict:
res = {}
if n % 2 == 0:
res[2] = 1
n //= 2
while n % 2 == 0:
res[2] += 1
n //= 2
if n % 3 == 0:
res[3] = 1
n //= 3
while n % 3 == 0:
res[3] += 1
n //= 3
k = 1
while n > 1:
for i in [-1, 1]:
d = 6 * k + i
if n % d == 0:
res[d] = 1
n //= d
while n % d == 0:
res[d] += 1
n //= d
k += 1
return res
def factorization(N: int, M: int) -> int:
"""以下の説明において、F(N, M) はこの関数と同値。
`a1 x a2 x ... x aN = M (式 1)`
となる数列 {aN} の組み合わせ数を F(N, M) とする。
まず、(式 1)より {aN} は全て M の約数であることは明らか。
ここで、M の約数列を {dm} とする。今、aN = di とすると、
`a1 x a2 x ... x a{N-1} = M // di`
が成り立ち、これを満たす数列 {a{N-1}} の組み合わせ数は F(N-1, M//di) である。
aN は任意の di を取れるので、結局、
`F(N, M) = sigma{di} F(N-1, M//di) = sigma{di} F(N-1, M)` (式 2)
が成り立つ。
さらに、M を場合分けして考える。
M = 1 のとき、(式 2)より
`F(N, 1) = F(N-1, 1) = ... = F(1, 1) = 1` (式 3)
が成り立つ。
M = p (p は素数)のとき、(式 2)と(式 3)より、
`F(N, p) = F(N-1, p) + F(N-1, 1) = F(N-1, p) + 1`
が成り立つ。この漸化式をとけば、
`F(N, p) = N`
が成り立つ。
M = p^k (p は素数)の時、めんどくさい計算の果てに
`F(N, p^k) = PI{i=0}{k-1}(N+i) / k!`
が成り立つ。
M = p1...pk (pi は全て異なる素数)の時、めんどくさい計算の果てに
`F(N,p1...pk) = N^k`
M = p1^k1 ... pm^km (pi は全て異なる素数)の時、めんどくさい計算の果てに
`F(N,p1^k1...pm^km) = F(N,p1^k1)...F(N,pm^km)`
が成り立つ。
"""
pi = [1] * 101
fact = [1] * 101
for i in range(1, 101):
pi[i] = (N+i-1) * pi[i-1]
fact[i] = i * fact[i-1]
primes = prime_facts(M)
ret = 1
for k in list(primes.values()):
ret *= pi[k] // fact[k]
return ret % 1000000007
if __name__ == "__main__":
N, M = list(map(int, input().split()))
ans = factorization(N, M)
print(ans)
| from math import sqrt
def prime_facts(n: int) -> dict:
res = {}
d = 2
while d * d <= n:
if n % d == 0:
res[d] = 1
n //= d
while n % d == 0:
res[d] += 1
n //= d
if d == 2:
d += 1
else:
d += 2
if n > 1:
res[n] = 1
return res
def factorization(N: int, M: int) -> int:
"""以下の説明において、F(N, M) はこの関数と同値。
`a1 x a2 x ... x aN = M (式 1)`
となる数列 {aN} の組み合わせ数を F(N, M) とする。
まず、(式 1)より {aN} は全て M の約数であることは明らか。
ここで、M の約数列を {dm} とする。今、aN = di とすると、
`a1 x a2 x ... x a{N-1} = M // di`
が成り立ち、これを満たす数列 {a{N-1}} の組み合わせ数は F(N-1, M//di) である。
aN は任意の di を取れるので、結局、
`F(N, M) = sigma{di} F(N-1, M//di) = sigma{di} F(N-1, M)` (式 2)
が成り立つ。
さらに、M を場合分けして考える。
M = 1 のとき、(式 2)より
`F(N, 1) = F(N-1, 1) = ... = F(1, 1) = 1` (式 3)
が成り立つ。
M = p (p は素数)のとき、(式 2)と(式 3)より、
`F(N, p) = F(N-1, p) + F(N-1, 1) = F(N-1, p) + 1`
が成り立つ。この漸化式をとけば、
`F(N, p) = N`
が成り立つ。
M = p^k (p は素数)の時、めんどくさい計算の果てに
`F(N, p^k) = PI{i=0}{k-1}(N+i) / k!`
が成り立つ。
M = p1...pk (pi は全て異なる素数)の時、めんどくさい計算の果てに
`F(N,p1...pk) = N^k`
M = p1^k1 ... pm^km (pi は全て異なる素数)の時、めんどくさい計算の果てに
`F(N,p1^k1...pm^km) = F(N,p1^k1)...F(N,pm^km)`
が成り立つ。
"""
# pi と fact の初期化
pi = [1] * 101
fact = [1] * 101
for i in range(1, 101):
pi[i] = (N+i-1) * pi[i-1]
fact[i] = i * fact[i-1]
primes = prime_facts(M)
ret = 1
for k in list(primes.values()):
ret *= pi[k] // fact[k]
return ret % 1000000007
if __name__ == "__main__":
N, M = list(map(int, input().split()))
ans = factorization(N, M)
print(ans)
| p03253 |
from collections import defaultdict as dd
import sys
import math
n, m = list(map(int, input().split()))
dic = dd(int)
#M=1
if m == 1:
print((1))
sys.exit()
elif n == 1:
print((1))
sys.exit()
def combinations_count(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
for i in range(2, math.ceil(m**0.5) + 3):
while m % i == 0:
m //= i
dic[i] += 1
else:
if m != 1:
dic[m] = 1
#print(dic)
ans = 1
mod = 10**9 + 7
for count in list(dic.values()):
ans *= combinations_count(count + n - 1, n-1) % mod
print((ans % mod)) | from collections import defaultdict as dd
from sys import exit
import math
n, m = list(map(int, input().split()))
dic = dd(int)
#M=1
if m == 1:
print((1))
exit()
def combinations_count(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
for i in range(2, math.ceil(m**0.5) + 3):
while m % i == 0:
m //= i
dic[i] += 1
if m != 1:
dic[m] = 1
#print(dic)
ans = 1
mod = 10**9 + 7
for count in list(dic.values()):
ans *= combinations_count(count + n - 1, n-1) % mod
print((ans % mod)) | p03253 |
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 = list(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)
| 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 = list(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)
| p03253 |
N,M=list(map(int,input().split()))
import math
a=[]
ans=1
def calc(n):#nの素因数分解
for i in range(2,int(n**0.5)+10):
count=0
while n%i==0:
n//=i
count+=1
if count>=1:
a.append([i,count])
if n!=1:
a.append([n,1])
def conb(n,k):
return math.factorial(n)//(math.factorial(n-k)*math.factorial(k))
calc(M)
for i in range(len(a)):
ans*=conb(a[i][1]+N-1,a[i][1])
print((ans%(10**9+7))) | N,M=list(map(int,input().split()))
a=[]
ans=1
def calc(n):#nの素因数分解
for i in range(2,int(n**0.5)+10):
count=0
while n%i==0:
n//=i
count+=1
if count>=1:
a.append([i,count])
if n!=1:
a.append([n,1])
calc(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
for i in range(len(a)):
ans*=cmb(a[i][1]+N-1,a[i][1])
print((ans%(10**9+7))) | p03253 |
from collections import defaultdict
def prepare(n, MOD):
f = 1
factorials = [1] * (n + 1)
for m in range(1, n + 1):
f *= m
f %= MOD
factorials[m] = f
inv = pow(f, MOD - 2, MOD)
invs = [1] * (n + 1)
invs[n] = inv
for m in range(n, 1, -1):
inv *= m
inv %= MOD
invs[m - 1] = inv
return factorials, invs
def prime_factorize(n):
f = defaultdict(lambda: 0)
f[2] = len(bin(n & -n)) - 3
i = 3
k = n >> f[2]
while k > 1:
while True:
d, m = divmod(k, i)
if m == 0:
f[i] += 1
k = d
else:
break
i += 2
return f
MOD = 1000000007
n, m = list(map(int, input().split()))
pf = prime_factorize(m)
mx = max(pf.values())
f, r = prepare(n + mx - 1, MOD)
ans = 1
for p, e in list(pf.items()):
ans *= f[n + e - 1]
ans %= MOD
ans *= r[n - 1]
ans %= MOD
ans *= r[e]
ans %= MOD
print(ans)
| from collections import defaultdict
def prepare(n, MOD):
f = 1
factorials = [1] * (n + 1)
for m in range(1, n + 1):
f *= m
f %= MOD
factorials[m] = f
inv = pow(f, MOD - 2, MOD)
invs = [1] * (n + 1)
invs[n] = inv
for m in range(n, 1, -1):
inv *= m
inv %= MOD
invs[m - 1] = inv
return factorials, invs
def prime_factorize(n):
f = defaultdict(lambda: 0)
f[2] = len(bin(n & -n)) - 3
i = 3
k = n >> f[2]
limit = k ** 0.5
while 1 < k and i <= limit:
while True:
d, m = divmod(k, i)
if m == 0:
f[i] += 1
k = d
else:
break
i += 2
if k > 1:
f[k] = 1
return f
MOD = 1000000007
n, m = list(map(int, input().split()))
pf = prime_factorize(m)
mx = max(pf.values())
f, r = prepare(n + mx - 1, MOD)
ans = 1
for p, e in list(pf.items()):
ans *= f[n + e - 1]
ans %= MOD
ans *= r[n - 1]
ans %= MOD
ans *= r[e]
ans %= MOD
print(ans)
| p03253 |
from collections import defaultdict
def prepare(n, MOD):
f = 1
factorials = [1] * (n + 1)
for m in range(1, n + 1):
f *= m
f %= MOD
factorials[m] = f
inv = pow(f, MOD - 2, MOD)
invs = [1] * (n + 1)
invs[n] = inv
for m in range(n, 1, -1):
inv *= m
inv %= MOD
invs[m - 1] = inv
return factorials, invs
def prime_factorize(n):
f = defaultdict(lambda: 0)
f[2] = len(bin(n & -n)) - 3
i = 3
k = n >> f[2]
limit = k ** 0.5
while 1 < k and i <= limit:
while True:
d, m = divmod(k, i)
if m == 0:
f[i] += 1
k = d
else:
break
i += 2
if k > 1:
f[k] = 1
return f
MOD = 1000000007
n, m = list(map(int, input().split()))
pf = prime_factorize(m)
mx = max(pf.values())
f, r = prepare(n + mx - 1, MOD)
ans = 1
for p, e in list(pf.items()):
ans *= f[n + e - 1]
ans %= MOD
ans *= r[n - 1]
ans %= MOD
ans *= r[e]
ans %= MOD
print(ans)
| from collections import defaultdict
def prepare(n, MOD):
f = 1
factorials = [1] * (n + 1)
for m in range(1, n + 1):
f *= m
f %= MOD
factorials[m] = f
inv = pow(f, MOD - 2, MOD)
invs = [1] * (n + 1)
invs[n] = inv
for m in range(n, 1, -1):
inv *= m
inv %= MOD
invs[m - 1] = inv
return factorials, invs
def prime_factorize(n):
f = defaultdict(lambda: 0)
f[2] = len(bin(n & -n)) - 3
i = 3
k = n >> f[2]
limit = k ** 0.5
while 1 < k and i <= limit:
while True:
d, m = divmod(k, i)
if m == 0:
f[i] += 1
k = d
limit = k ** 0.5
else:
break
i += 2
if k > 1:
f[k] = 1
return f
MOD = 1000000007
n, m = list(map(int, input().split()))
pf = prime_factorize(m)
mx = max(pf.values())
f, r = prepare(n + mx - 1, MOD)
ans = 1
for p, e in list(pf.items()):
ans *= f[n + e - 1]
ans %= MOD
ans *= r[n - 1]
ans %= MOD
ans *= r[e]
ans %= MOD
print(ans)
| p03253 |
n,m=list(map(int,input().split()))
def c(n,m):
import math
if n-m<0:
return 0
return(math.factorial(n)//math.factorial(n-m)//math.factorial(m))
def factorize(n):
fct=[]
b,e=2,0
while b*b<=n:
while n%b==0:
n=n//b
e=e+1
if e>0:
fct.append((b,e))
b,e=b+1,0
if n>1:
fct.append((n,1))
return fct
l=factorize(m)
mod=10**9+7
ans=1
for i,j in l:
ans*=c(j+n-1,j)
ans=ans%mod
print(ans) | n,m=list(map(int,input().split()))
def factorize(n):
fct=[]
b,e=2,0
while b*b<=n:
while n%b==0:
n=n//b
e=e+1
if e>0:
fct.append((b,e))
b,e=b+1,0
if n>1:
fct.append((n,1))
return fct
l=factorize(m)
mod=10**9+7
ans=1
def inv(x):
return pow(x, mod - 2, mod)
cms = 10**5 + 100
cm = [0] * cms
def comb_init():
cm[0] = 1
for i in range(1, cms):
cm[i] = cm[i-1] * i % mod
def c(a, b):
return (cm[a] * inv(cm[a-b]) % mod) * inv(cm[b]) % mod
mod=10**9+7
comb_init()
for i,j in l:
ans*=c(j+n-1,j)
ans=ans%mod
print(ans) | p03253 |
def soin(num):
re = []
div = 2
while 1:
lim = int(num ** 0.5) + 1
while num % div:
div += 1
if div > lim:
re += [1]
return re
sisu = 0
while num % div == 0:
num //= div
sisu += 1
re += [sisu]
if num == 1:
return re
def com(a, b):
if a == b:
return 1
t = (a, b)
if (a, b) in com_memo:
return com_memo[t]
re = com(a - 1, b) * a // (a - b)
com_memo[t] = re
return re
def f(n, m):
sisus = soin(m)
ans = 1
for s in sisus:
ans = ans * com(s + n - 1, n - 1) % md
print(ans)
md = 10 ** 9 + 7
n, m = list(map(int, input().split()))
if m==1:
print((1))
exit()
com_memo = {}
f(n, m)
| def soin(num):
re = []
div = 2
while 1:
lim = int(num ** 0.5) + 1
while num % div:
div += 1
if div > lim:
re += [1]
return re
sisu = 0
while num % div == 0:
num //= div
sisu += 1
re += [sisu]
if num == 1:
return re
def com(a, b):
if a == b:
return 1
t = (a, b)
if (a, b) in com_memo:
return com_memo[t]
re = com(a - 1, b) * a // (a - b)
com_memo[t] = re
return re
def f(n, m):
if m == 1:
print((1))
return
sisus = soin(m)
ans = 1
for s in sisus:
ans = ans * com(s + n - 1, n - 1) % md
print(ans)
md = 10 ** 9 + 7
n, m = list(map(int, input().split()))
com_memo = {}
f(n, m)
| p03253 |
import sys
readline = sys.stdin.buffer.readline
from collections import Counter
n,m = list(map(int,readline().split()))
mod = 10**9+7
"""素因数分解"""
def factrize(n):
b = 2
fct = []
while b*b <= n:
while n % b == 0:
n //= b
#もし素因数を重複させたくないならここを加えてfct.append(b)を消す
"""
if not b in fct:
fct.append(b)
"""
fct.append(b)
b = b+1
if n > 1:
fct.append(n)
return fct #リストが帰る
def pow(n,p,mod=10**9+7): #繰り返し二乗法(nのp乗)
res = 1
while p > 0:
if p % 2 == 0:
n = n ** 2 % mod
p //= 2
else:
res = res * n % mod
p -= 1
return res % mod
def factrial_memo(n=20**5+1,mod=10**9+7):
fact = [1, 1]
for i in range(2, n + 1):
fact.append((fact[-1] * i) % mod)
return fact
fact = factrial_memo()
def fermat_cmb(n, r, mod=10**9+7): #needs pow,factrial_memo(only fact). return nCk
return fact[n] * pow(fact[r],mod-2) * pow(fact[n-r],mod-2) %mod
lst1 = factrize(m)
c = Counter(lst1)
ans = 1
for i in list(c.values()):
ans *= fermat_cmb(n+i-1,i)
ans %= mod
print(ans)
| import sys
readline = sys.stdin.buffer.readline
def even(n): return 1 if n%2==0 else 0
"""
1*1*1*1*m = mなども含める
4をそのまま使う場合と2*2に分ける場合などの場合分けが必要
約数列挙からどうこうする？
"""
n,m = list(map(int,readline().split()))
mod = 10**9+7
def pow(n,p,mod=10**9+7): #繰り返し二乗法(nのp乗)
res = 1
while p > 0:
if p % 2 == 0:
n = n ** 2 % mod
p //= 2
else:
res = res * n % mod
p -= 1
return res % mod
def factrial_memo(n=10**6,mod=10**9+7):
fact = [1, 1]
for i in range(2, n + 1):
fact.append((fact[-1] * i) % mod)
return fact
fact = factrial_memo()
"""素因数分解"""
def factrize(n):
b = 2
fct = []
while b*b <= n:
while n % b == 0:
n //= b
#もし素因数を重複させたくないならここを加えてfct.append(b)を消す
"""
if not b in fct:
fct.append(b)
"""
fct.append(b)
b = b+1
if n > 1:
fct.append(n)
return fct #リストが帰る
prime = factrize(m)
from collections import defaultdict
dic1 = defaultdict(int)
for i in prime:
dic1[i] += 1
ans = 1
for i in list(dic1.values()):
ans *= fact[n+i-1]*pow(fact[n-1],mod-2)*pow(fact[i],mod-2)
ans %= mod
print(ans) | p03253 |
# https://atcoder.jp/contests/abc110/tasks/abc110_d
def get_prime_dic(n):
dic = {}
while n % 2 == 0:
if 2 in dic:
dic[2] += 1
else:
dic[2] = 1
n = n // 2
i = 3
while i <= n:
while n % i == 0:
n //= i
if i in dic:
dic[i] += 1
else:
dic[i] = 1
i += 2
if n > 1:
dic[n] = 1
return dic
# Calculate count of combination
def combination(n, r):
a = 1
b = 1
for i in range(r):
a *= (n - i)
b *= (i + 1)
return a // b
def main():
N, M = list(map(int, input().split()))
d = get_prime_dic(M)
# print(d)
ans = 1
for k, v in list(d.items()):
ans *= combination(v + N - 1, v)
ans %= 1000000007
print(ans)
main()
| N, M = [int(i) for i in input().split()]
mod = 10 ** 9 + 7
def func(M):
res = []
i = 2
while i * i <= M:
c=0
while M % i == 0:
M /= i
c += 1
if c > 0:
res.append(c)
i += 1
if M > 1:
res.append(1)
return res
def conb(n, r):
N, R = n, r
for i in range(1, r):
N *= n-i
R *= r-i
return N // R
res = func(M)
ans = 1
for i in res:
ans = (ans * conb(i+N-1, i)) % mod
print(ans)
| p03253 |
from math import factorial as fact
import sys
input = sys.stdin.readline
N, M = list(map(int, input().split()))
num = []
p_flag = [True]*(int(M**0.5)+2)
for i in range(2, int(M**0.5)+2):
if p_flag:
for j in range(2*i, int(M**0.5)+2, i):
p_flag[j] = False
cnt = 0
while M % i == 0:
cnt += 1
M //= i
if cnt > 0:
num.append(cnt)
if M == 1:
break
else:
num.append(1)
ans = 1
for i in num:
ans = (ans * fact(N-1+i)//(fact(i)*fact(N-1))) % (10**9+7)
print(ans) | from math import factorial as fact
from operator import mul
from functools import reduce
import sys
input = sys.stdin.readline
def cmb(n,r):
r = min(n-r,r)
if r == 0: return 1
over = reduce(mul, list(range(n, n - r, -1)))
under = reduce(mul, list(range(1,r + 1)))
return over // under
N, M = list(map(int, input().split()))
num = []
p_flag = [True]*(int(M**0.5)+2)
for i in range(2, int(M**0.5)+2):
if p_flag:
for j in range(2*i, int(M**0.5)+2, i):
p_flag[j] = False
cnt = 0
while M % i == 0:
cnt += 1
M //= i
if cnt > 0:
num.append(cnt)
if M == 1:
break
else:
num.append(1)
ans = 1
for i in num:
ans = (ans * cmb(N-1+i, i)) % (10**9+7)
print(ans) | p03253 |
import math
from collections import Counter
from functools import reduce
from operator import mul
def get_factors(n):
"""
素因数分解
:param int n:
:type: list of int
"""
if n <= 1:
return []
ret = []
while n > 2 and n % 2 == 0:
ret.append(2)
n //= 2
i = 3
while i <= n / 2:
if n % i == 0:
ret.append(i)
n //= i
else:
i += 2
ret.append(n)
return ret
def comb(n, r):
"""
組み合わせの数 nCr
:param n:
:param r:
:return:
"""
r = min(n - r, r)
if r == 0:
return 1
return reduce(mul, list(range(n, n - r, -1))) // reduce(mul, list(range(r, 0, -1)))
n, m = list(map(int, input().split()))
MOD = 10 ** 9 + 7
# divs = sorted(get_divisors(m))
# # dp[d]: 累積積が d となる数列の数
# dp = {d: 1 for d in divs}
# for _ in range(n - 1):
# for i in reversed(range(len(divs))):
# div = divs[i]
# dp[div] = sum([dp[d] for d in divs if div % d == 0]) % MOD
# print(dp)
# print(dp)
# おそい
factors = get_factors(m)
counts = Counter(factors)
# k**v を全部かけあわせたやつが m に一致する
# print(functools.reduce(operator.mul, [k ** v for k, v in counts.items()]))
# v 個の k を n 個の数に配分する組み合わせの数
# → v + (n-1) 個のスペースへの v の置き方の組み合わせの数
ans = 1
for k, v in list(counts.items()):
ans *= comb(v + (n - 1), v)
ans %= MOD
print(ans)
| import math
from collections import Counter
from functools import reduce
from operator import mul
def get_factors(n):
"""
素因数分解
:param int n:
:type: list of int
"""
if n <= 1:
return []
ret = []
while n > 2 and n % 2 == 0:
ret.append(2)
n //= 2
i = 3
while i <= math.sqrt(n):
if n % i == 0:
ret.append(i)
n //= i
else:
i += 2
ret.append(n)
return ret
def comb(n, r):
"""
組み合わせの数 nCr
:param n:
:param r:
:return:
"""
r = min(n - r, r)
if r == 0:
return 1
return reduce(mul, list(range(n, n - r, -1))) // reduce(mul, list(range(r, 0, -1)))
n, m = list(map(int, input().split()))
MOD = 10 ** 9 + 7
# divs = sorted(get_divisors(m))
# # dp[d]: 累積積が d となる数列の数
# dp = {d: 1 for d in divs}
# for _ in range(n - 1):
# for i in reversed(range(len(divs))):
# div = divs[i]
# dp[div] = sum([dp[d] for d in divs if div % d == 0]) % MOD
# print(dp)
# print(dp)
# おそい
factors = get_factors(m)
counts = Counter(factors)
# k**v を全部かけあわせたやつが m に一致する
# print(functools.reduce(operator.mul, [k ** v for k, v in counts.items()]))
# v 個の k を n 個の数に配分する組み合わせの数
# → v + (n-1) 個のスペースへの v の置き方の組み合わせの数
ans = 1
for k, v in list(counts.items()):
ans *= comb(v + (n - 1), v)
ans %= MOD
print(ans)
| p03253 |
import math
import os
import sys
from collections import Counter
if os.getenv("LOCAL"):
sys.stdin = open("_in.txt", "r")
sys.setrecursionlimit(2147483647)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7
N, M = list(map(int, sys.stdin.readline().split()))
def get_factors(n):
"""
素因数分解
:param int n:
:rtype: list of int
"""
if n <= 1:
return []
ret = []
while n > 2 and n % 2 == 0:
ret.append(2)
n //= 2
i = 3
while i <= math.sqrt(n):
if n % i == 0:
ret.append(i)
n //= i
else:
i += 2
ret.append(n)
return ret
def ncr(n, r, mod=None):
"""
scipy.misc.comb または scipy.special.comb と同じ
組み合わせの数 nCr
:param int n:
:param int r:
:param int mod: 3 以上の素数であること
:rtype: int
"""
if n < r:
return 0
return math.factorial(n) // math.factorial(r) // math.factorial(n - r)
factors = get_factors(M)
ans = 1
for c in list(Counter(factors).values()):
# N 個の箱から重複ありで c 個選ぶ
ans = ans * ncr(N + c - 1, c) % MOD
print(ans)
| import math
import os
import sys
from collections import Counter
from functools import reduce
from operator import mul
if os.getenv("LOCAL"):
sys.stdin = open("_in.txt", "r")
sys.setrecursionlimit(2147483647)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7
N, M = list(map(int, sys.stdin.readline().split()))
def get_factors(n):
"""
素因数分解
:param int n:
:rtype: list of int
"""
if n <= 1:
return []
ret = []
while n > 2 and n % 2 == 0:
ret.append(2)
n //= 2
i = 3
while i <= math.sqrt(n):
if n % i == 0:
ret.append(i)
n //= i
else:
i += 2
ret.append(n)
return ret
def ncr(n, r, mod=None):
"""
scipy.misc.comb または scipy.special.comb と同じ
組み合わせの数 nCr
:param int n:
:param int r:
:param int mod: 3 以上の素数であること
:rtype: int
"""
if n < r:
return 0
r = min(n - r, r)
if r == 0:
return 1
return reduce(mul, list(range(n, n - r, -1))) // reduce(mul, list(range(r, 0, -1)))
factors = get_factors(M)
ans = 1
for c in list(Counter(factors).values()):
# N 個の箱から重複ありで c 個選ぶ
ans = ans * ncr(N + c - 1, c) % MOD
print(ans)
| p03253 |
from math import factorial as f
N, M = list(map(int, input().split()))
a1, a2 = 2, M
a = {}
while (a1 - 1) ** 2 <= a2 or a1 == a2:
if a2 % a1 == 0:
a2 //= a1
if a1 in a:
a[a1] += 1
else:
a[a1] = 1
else:
a1 += 1
p = 1
if a2 != 1:
a[a2] = 1
for v in list(a.values()):
p *= f(v + N - 1) // (f(v) * f(N - 1))
print((p % (10 ** 9 + 7))) | N, M = list(map(int, input().split()))
a1, a2 = 2, M
a = {}
while (a1 - 1) ** 2 <= a2 or a1 == a2:
if a2 % a1 == 0:
a2 //= a1
if a1 in a:
a[a1] += 1
else:
a[a1] = 1
else:
a1 += 1
p = 1
if a2 != 1:
a[a2] = 1
for v in list(a.values()):
tmp = 1
for i in range(v):
tmp = tmp * (v + N - 1 - i) // (i + 1)
p *= tmp
print((p % (10 ** 9 + 7))) | p03253 |
import math
def prime_division(n):
ans = []
m = int(n ** 0.5)
i = 2
while i <= m:
if n % i == 0:
cnt = 0
while n % i == 0:
n //= i
cnt += 1
ans.append((i, cnt))
m = int(n ** 0.5)
i += 1
if n != 1:
ans.append((n, 1))
return ans
# aabaaba count+(N-1) C (N-1)
N,M=list(map(int,input().split()))
pms=prime_division(M)
ans = 1
for pm in pms:
#print(pm)
ans *= math.factorial(pm[1]+(N-1)) // (math.factorial(pm[1]) * math.factorial(N-1))
print((ans % (10 ** 9 + 7)))
| import math
def prime_division(n):
ans = []
m = int(n ** 0.5)
i = 2
while i <= m:
if n % i == 0:
cnt = 0
while n % i == 0:
n //= i
cnt += 1
ans.append((i, cnt))
m = int(n ** 0.5)
i += 1
if n != 1:
ans.append((n, 1))
return ans
def combination(n, r):
ans = 1
if n - r < r:
r = n - r
for i in range(r):
ans *= n - i
ans //= math.factorial(r)
return ans
# aabaaba count+(N-1) C (N-1)
N,M=list(map(int,input().split()))
pms=prime_division(M)
ans = 1
for pm in pms:
#print(pm)
ans *= combination(pm[1]+(N-1), N-1)
print((ans % (10 ** 9 + 7)))
| p03253 |
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 list(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 = list(map(int, input().split()))
r = 1
prime_fac = prime_factorize(m)
for v in list(prime_fac.values()):
r *= comb(v+n-1, v)
mod = 1000000000 + 7
print((r % mod))
| 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 list(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, R):
if n not in R:
a = factorial(n)
R[n] = a
else:
a = R[n]
if n - r not in R:
b = factorial(n - r)
R[n - r] = b
else:
b = R[n - r]
if r not in R:
c = factorial(r)
R[r] = c
else:
c = R[r]
return a // (b * c)
n, m = list(map(int, input().split()))
r = 1
R = dict()
prime_fac = prime_factorize(m)
for v in list(prime_fac.values()):
r *= comb(v + n - 1, v, R)
mod = 1000000000 + 7
print((r % mod))
| p03253 |
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 list(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, R):
if n not in R:
a = factorial(n)
R[n] = a
else:
a = R[n]
if n - r not in R:
b = factorial(n - r)
R[n - r] = b
else:
b = R[n - r]
if r not in R:
c = factorial(r)
R[r] = c
else:
c = R[r]
return a // (b * c)
n, m = list(map(int, input().split()))
r = 1
R = dict()
prime_fac = prime_factorize(m)
for v in list(prime_fac.values()):
r *= comb(v + n - 1, v, R)
mod = 1000000000 + 7
print((r % mod))
| 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 list(prime_factor.keys()):
prime_factor[i] += 1
else:
prime_factor[i] = 1
i += 1
if num > 1:
prime_factor[num] = 1
return prime_factor
def combination(n, r):
r = min(n-r, r)
result = 1
for i in range(n, n-r, -1):
result *= i
for i in range(1, r+1):
result //= i
return result
n, m = list(map(int, input().split()))
r = 1
prime_fac = prime_factorize(m)
for v in list(prime_fac.values()):
r *= combination(v + n - 1, v)
mod = 1000000000 + 7
print((r % mod))
| p03253 |
N, M = list(map(int, input().split()))
MAX_NUM = 10 ** 9 + 7
def func(M):
res = []
i, c = 2, 0
while True:
if M % i == 0:
M = M / i
c+=1
else:
if c > 0:
res.append(c)
c = 0
i += 1
if M==1:
break
return res
def conb(n, r):
N, R = n, r
for i in range(1, r):
N *= n-i
R *= r-i
return N // R
res = func(M)
ans = 1
for i in res:
ans = (ans * conb(i+N-1, i)) % MAX_NUM
print(ans) | N, M = [int(i) for i in input().split()]
mod = 10 ** 9 + 7
def func(M):
res = []
i = 2
while i * i <= M:
c=0
while M % i == 0:
M /= i
c += 1
if c > 0:
res.append(c)
i += 1
if M > 1:
res.append(1)
return res
def conb(n, r):
N, R = n, r
for i in range(1, r):
N *= n-i
R *= r-i
return N // R
res = func(M)
ans = 1
for i in res:
ans = (ans * conb(i+N-1, i)) % mod
print(ans) | p03253 |
import math
def comb(x,y):
f = 1
for i in range(y):
f *= (x-i)
f //= (i+1)
return f
n,m = list(map(int,input().split()))
cnt = [0]
for i in range(2,m+1):
while m!=i:
if m%i==0:
m //=i
cnt[-1]+=1
else:
cnt.append(0)
break
if m==i:
cnt[-1]+=1
break
cnt = [item for item in cnt if cnt != 0]
res = 1
r = 10**9 +7
for item in cnt:
res = (res* comb(item+n-1,item))%r
print((res%r))
| import math
def comb(x,y):
f = 1
for i in range(y):
f *= (x-i)
f //= (i+1)
return f
n,m = list(map(int,input().split()))
i = 2
cnt = []
while i*i<=m:
c = 0
while m%i == 0:
m //= i
c += 1
if c>0:
cnt.append(c)
i+=1
if m>1:
cnt.append(1)
res = 1
r = 10**9 +7
for item in cnt:
res = (res* comb(item+n-1,item))%r
print((res%r))
| p03253 |
import collections
from functools import reduce
from operator import mul
def trial_division(n):
l = []
f = 2
while n > 1:
if n % f == 0:
l.append(f)
n /= f
else:
f += 1
return l
def combinations_count(n, r):
r = min(n - r, r)
if r == 0:
return 1
return reduce(mul, list(range(n, n - r, -1))) // reduce(mul, list(range(r, 0, -1)))
N, M = list(map(int, input().split()))
c = collections.Counter(trial_division(M))
a = 1
for i in list(c.values()):
a *= combinations_count(i + N - 1, i)
print((a % (10**9 + 7)))
| import collections
from functools import reduce
from operator import mul
def trial_division(n):
l = []
f = 2
while f * f <= n:
if n % f == 0:
l.append(f)
n //= f
else:
f += 1
if n > 1:
l.append(n)
return l
def combinations_count(n, r):
r = min(n - r, r)
if r == 0:
return 1
return reduce(mul, list(range(n, n - r, -1))) // reduce(mul, list(range(r, 0, -1)))
N, M = list(map(int, input().split()))
c = collections.Counter(trial_division(M))
a = 1
for i in list(c.values()):
a *= combinations_count(i + N - 1, i)
print((a % (10**9 + 7))) | p03253 |
from math import sqrt
N, M = [int(_) for _ in input().split()]
p = []
m = M
max_x = 1
for i in range(2, int(sqrt(m)) + 1):
if m % i == 0:
cnt = 0
while m % i == 0:
cnt += 1
m //= i
p.append((i, cnt))
if cnt > max_x:
max_x = cnt
if m > 1:
p.append((m, 1))
kaijo = [0] * (max_x + 1 + N)
gyaku = [0] * (max_x + 1 + N)
kaijo[0] = kaijo[1] = 1
gyaku[0] = gyaku[1] = 1
MOD = 10 ** 9 + 7
for i in range(2, len(kaijo)):
kaijo[i] = (kaijo[i - 1] * i) % MOD
for i in range(2, len(gyaku)):
gyaku[i] = pow(kaijo[i], MOD - 2, MOD)
# print(kaijo)
# print(gyaku)
ans = 1
for x, y in p:
a = y + (N - 1)
b = (N - 1)
spam = (kaijo[a] * gyaku[a - b] * gyaku[b]) % MOD
ans = (ans * spam) % MOD
print(ans)
| def prime_factorization(n):
"""
nを素因数分解
:param n:
:return:素因数分解結果 [(素数S1, count S1),(素数S2, count S2), ...]
"""
from math import sqrt
if (n == 0): return []
if (n == 1): return [(1, 1)]
res = []
for i in range(2, int(sqrt(n)) + 1):
if n == 1: break
cnt = 0
while n % i == 0:
cnt += 1
n = n // i
if cnt > 0:
res.append((i, cnt))
if n > 1:
res.append((n, 1))
return res
class ModFactorial:
"""
階乗, 組み合わせ, 順列の計算
"""
def __init__(self, n, MOD=10 ** 9 + 7):
"""
:param n: 最大の要素数.
:param MOD:
"""
kaijo = [0] * (n + 10)
gyaku = [0] * (n + 10)
kaijo[0] = 1
kaijo[1] = 1
for i in range(2, len(kaijo)):
kaijo[i] = (i * kaijo[i - 1]) % MOD
gyaku[0] = 1
gyaku[1] = 1
for i in range(2, len(gyaku)):
gyaku[i] = pow(kaijo[i], MOD - 2, MOD)
self.kaijo = kaijo
self.gyaku = gyaku
self.MOD = MOD
def nCm(self, n, m):
return (self.kaijo[n] * self.gyaku[n - m] * self.gyaku[m]) % self.MOD
def nPm(self, n, m):
return (self.kaijo[n] * self.gyaku[n - m]) % self.MOD
def factorial(self, n):
return self.kaijo[n]
N, M = [int(_) for _ in input().split()]
if M == 1:
print((1))
exit()
primes = [v for _, v in prime_factorization(M)]
MOD = 10 ** 9 + 7
mf = ModFactorial(max(primes) + 1 + N, MOD)
ans = 1
for cnt in primes:
ans = ans * mf.nCm(cnt + N - 1, N - 1)
ans = ans % MOD
print(ans)
| p03253 |
# -*- 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(eval(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
else:
ans *= nCr(n+N-1,N-1)
ans %= MOD
print(ans) | # -*- 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(eval(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:
ans *= nCr(n+N-1,N-1)
ans %= MOD
print(ans) | p03253 |
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 = list(map(int, input().split()))
if m == 1:
print((1))
return
fac = factorization(m)
prime_combs = []
for prime, cnt in list(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() | 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
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():
n,m = list(map(int, input().split()))
if m == 1:
print((1))
exit()
facd = factorization(m)
com_init()
ans = 1
for k,v in list(facd.items()):
comb = com(v+n-1,n-1)
ans *= comb
ans%=MOD
print(ans)
if __name__ == "__main__":
main() | p03253 |
from math import factorial
from math import sqrt
def nCr(n,r):
return factorial(n)//(factorial(r)*factorial(n-r))
"""
def factorize(p):
b=[]
for i in range(2,int(sqrt(p)+2)):
a=0
while((p%i)==0):
a+=1
p=p//i
if a!=0:
b.append(a)
if p==1:
break
return b
"""
INF=10**9+7
N,m=list(map(int,input().split()))
sum=1
#B=factorize(M)
yd = {}
i = 2
while m != 1:
while m % i == 0:
if i in yd:
yd[i] += 1
else:
yd[i] = 1
m //= i
i += 1
for b in list(yd.values()):
sum*=nCr(N-1+b,N-1)
sum%=INF
print(sum)
| from math import factorial
from math import sqrt
def nCr(n,r):
a=1
x=n
while(x!=n-r):
a*=x
x-=1
b=1
x=r
while(x!=0):
b*=x
x-=1
return a//b
INF=10**9+7
N,m=list(map(int,input().split()))
sum=1
yd = {}
i = 2
while m != 1:
while m % i == 0:
if i in yd:
yd[i] += 1
else:
yd[i] = 1
m //= i
i += 1
for b in list(yd.values()):
sum*=nCr(N-1+b,b)
sum%=INF
print(sum)
| p03253 |
import math
n, m = list(map(int, input().split()))
mod = 10**9+7
def prime_decomposition(n):
p = 2
prime = {}
while n!=1:
while n%p == 0:
n = n//p
if p not in prime:
prime[p] = 0
prime[p] += 1
p += 1
return prime
primes = prime_decomposition(m)
ans = 1
def combination(n,k):
ret1 = 1
ret2 = 1
for i in range(k):
ret1 *= n-i
ret2 *= k-i
return ret1//ret2
for pw in list(primes.values()):
comb = combination(pw+n-1, pw)
ans *= comb
ans %= mod
print(ans)
| n, m = list(map(int, input().split()))
mod = 10**9+7
def prime_decomposition(n):
p = 2
prime = {}
while n!=1:
while n%p == 0:
n = n//p
if p not in prime:
prime[p] = 0
prime[p] += 1
p += 1
return prime
primes = prime_decomposition(m)
# print(primes)
ans = 1
def combination(n,k):
ret1 = 1
ret2 = 1
for i in range(k):
ret1 *= n-i
ret2 *= k-i
return ret1//ret2
for pw in list(primes.values()):
comb = combination(pw+n-1, pw)
ans *= comb
ans %= mod
print(ans)
| p03253 |
from collections import Counter
import math
n,m = list(map(int, input().split()))
def combinations_count(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def prime_decomposition(n, table):
i = 2
while i * i <= n:
while n % i == 0:
n /= i
table.append(i)
i += 1
if n > 1:
table.append(n)
table = []
prime_decomposition(m, table)
c = list(Counter(table).values())
cc = Counter(c)
ans = 1
N = n-1
for i,j in list(cc.items()):
ans *= ((combinations_count(N+i,i))**j)%(10**9+7)
print((ans%(10**9+7)))
| from collections import Counter
import math
n,m = list(map(int, input().split()))
def combinations_count(n, r):
l = 1
for num in range(1,r+1):
l *= (n+num)
l = l // num
return l
def prime_decomposition(n, table):
i = 2
while i * i <= n:
while n % i == 0:
n /= i
table.append(i)
i += 1
if n > 1:
table.append(n)
table = []
prime_decomposition(m, table)
c = list(Counter(table).values())
cc = Counter(c)
ans = 1
N = n-1
for i,j in list(cc.items()):
ans *= ((combinations_count(N,i))**j)%(10**9+7)
print((ans%(10**9+7))) | p03253 |
N,M=list(map(int,input().split()))
mod=10**9+7
from math import factorial
from collections import Counter
def soinsuu(n):
list_=[]
while(n!=1):
for i in range(2,int(n**0.5)+1):
if n%i==0:
list_.append(i)
n=n//i
break
else:
list_.append(n)
n=1
return sorted(list_)
def product(a):
pro=1
for b in a:
pro=pro*b%mod
return pro
#n!,nPr,nCrの高速計算
def n_func(n,mod=10**9+7):
ans=1
for i in range(1,n+1):
ans=(ans*i)%mod
return ans
def inv_n(n,mod=10**9+7):
return pow(n,mod-2,mod)
def nPr(n,r,mod=10**9+7):
ans=n_func(n-r,mod)
ans=inv_n(ans,mod)
return ans*n_func(n,mod)%mod
nPr_list=[nPr(N,i) for i in range(30)]
bunbo_list=dict()
def dp(cur,init,seq,lest,num):
#print(cur,init,seq,lest,num)
if cur==N:
if lest==0:
cnt=sorted(list(Counter(seq).values())+[N-len(seq)],reverse=True)
bunbo=product(list(map(factorial,cnt[1:])))
if bunbo not in list(bunbo_list.keys()):
bunbo_list[bunbo]=inv_n(bunbo)
memo[num]=(memo[num]+nPr_list[N-cnt[0]]*bunbo_list[bunbo])%mod
elif lest==0:
dp(N,init,seq,0,num)
else:
if cur==0:
for i in range(1,lest+1):
dp(cur+1,init,seq+[i],lest-i,num)
else:
for i in range(1,min(lest,seq[-1])+1):
dp(cur+1,init,seq+[i],lest-i,num)
p=list(Counter(soinsuu(M)).values())
memo=[0]*len(p)
for i in range(len(p)):
dp(0,p[i],[],p[i],i)
print((product(memo))) | N,M=list(map(int,input().split()))
from collections import Counter
def soinsuu(n):
list_=[]
while(n!=1):
for i in range(2,int(n**0.5)+1):
if n%i==0:
list_.append(i)
n=n//i
break
else:
list_.append(n)
n=1
return sorted(list_)
def product(a):
pro=1
for b in a:
pro=pro*b%(10**9+7)
return pro
#n!,nPr,nCrの高速計算
def n_func(n,mod=10**9+7):
ans=1
for i in range(1,n+1):
ans=(ans*i)%mod
return ans
def inv_n(n,mod=10**9+7):
return pow(n,mod-2,mod)
def nPr(n,r,mod=10**9+7):
ans=n_func(n-r,mod)
ans=inv_n(ans,mod)
return ans*n_func(n,mod)%mod
def nCr(n,r,mod=10**9+7):
ans=n_func(n-r,mod)*n_func(r,mod)%mod
ans=inv_n(ans,mod)
return ans*n_func(n,mod)%mod
p=list(Counter(soinsuu(M)).values())
print((product([nCr(N+p[i]-1,p[i]) for i in range(len(p))]))) | p03253 |
from math import factorial as fac
from collections import defaultdict as ddict
n,m = list(map(int,input().split()))
d = ddict(int)
ans = 1
mod = 10**9+7
def cc(n,r):
return fac(n)//fac(r)//fac(n-r)
for i in range(2,int(m**.5)+1):
while m % i == 0:
d[i] += 1
m //= i
if m > 1:
d[m] += 1
for x in d:
ans = ans * cc(d[x]+n-1,d[x])%mod
print(ans) | from math import factorial as fac
from collections import defaultdict as ddict
n,m = list(map(int,input().split()))
d = ddict(int)
ans = 1
mod = 10**9+7
def f2(n,r):
ret = 1
for i in range(n,n-r,-1):
ret *= i
return ret
def cc(n,r):
t = min(r,n-r)
return f2(n,t)//fac(t)
for i in range(2,int(m**.5)+1):
while m % i == 0:
d[i] += 1
m //= i
if m > 1:
d[m] += 1
for x in d:
ans = ans * cc(d[x]+n-1,d[x])%mod
print(ans) | p03253 |
from math import factorial
N, M = list(map(int,input().split()))
# 素因数分解(小さい方から順に割っていく。sqrt(2)まで)
def factorize(n):
i = 2
table = [0]
cnt= [0]
while i * i <= n:
while n % i == 0:
n /= i
if table[-1] != i:
table.append(i)
cnt.append(0)
cnt[-1] += 1
i += 1
if n > 1:
table.append(n)
cnt.append(1)
return table,cnt
# 組み合わせ
def combination(N,M):
return factorial(N)//(factorial(M)*factorial(N-M))
fs,ns = factorize(M)
ans = 1
for n in ns[1:]:
ans *= combination(n+N-1,n)
print((ans%(10**9+7))) | from math import factorial
N, M = list(map(int,input().split()))
# 素因数分解(小さい方から順に割っていく。sqrt(2)まで)
def factorize(n):
i = 2
table = [0]
cnt= [0]
while i * i <= n:
while n % i == 0:
n /= i
if table[-1] != i:
table.append(i)
cnt.append(0)
cnt[-1] += 1
i += 1
if n > 1:
table.append(n)
cnt.append(1)
return table,cnt
fs,ns = factorize(M)
ans = 1
for n in ns[1:]:
a = 1
for i in range(N,n+N):
a *= i
ans *= a//factorial(n)
print((ans%(10**9+7)))
| p03253 |
from math import sqrt, floor
from collections import defaultdict
def comb(n,m):
if m == 0:
return 1
return comb(n-1,m-1)*n // m
def facts(n):
dic = defaultdict(int)
for i in range(2,floor(sqrt(n))+1):
while n % i == 0:
n //= i
dic[i] += 1
if n == 1:
break
if n != 1:
dic[n] += 1
return dic
N, M = list(map(int,input().split()))
mod = 10**9+7
ans = 1
dic = facts(M)
for p in dic:
ans = (ans*(comb(dic[p]+N-1, dic[p]) % mod)) % mod
print(ans)
| from math import sqrt,floor
def comb(n,m):
if m == 0:
return 1
return comb(n-1,m-1)*n // m
n,m=list(map(int,input().split()))
mod=10**9+7
def factorization(x):
ans=[]
for i in range(2,floor(sqrt(x))+1):
if x%i==0:
cnt=0
while x%i==0:
x//=i
cnt+=1
ans.append([i,cnt])
if x==1:
break
if x!=1:
ans.append([x,1])
return ans
g=factorization(m)
ans=1
for i in g:
ans=(ans*(comb(i[1]+n-1,i[1])%mod))%mod
print(ans) | p03253 |
import math
def ncr(n,r):
return math.factorial(n)//(math.factorial(n-r)*math.factorial(r))
def factorize(n):
d = {}
m = 2
while m*m <= n:
if n%m == 0:
d[m] = 0
while n%m == 0:
n //= m
d[m] += 1
m += 1
if n > 1:
d[n] = 1
return d
count = 1
n,m = list(map(int,input().split()))
mod = 10**9+7
b = factorize(m)
for i in b:
count *= ncr(b[i]+n-1,b[i])%mod
print((count%mod)) | N,M = list(map(int,input().split()))
MOD = 10**9+7
from collections import Counter
c = Counter()
m = 2
while(m**2 <= M):
if M%m == 0:
while(M%m == 0):
c[m] += 1
M //= m
else:
m += 1
if M > 1 : c[M] += 1
MAXN = N+100
fac = [0 for _ in range(MAXN)]
inv = [0 for _ in range(MAXN)]
finv = [0 for _ in range(MAXN)]
fac[0] = fac[1] = 1
inv[1] = 1
finv[0] = finv[1] = 1
for i in range(2,MAXN):
fac[i] = (i*fac[i-1]) % MOD
inv[i] = (-inv[MOD%i]*(MOD//i))%MOD
finv[i] = (finv[i-1]*inv[i])%MOD
def comb(n,k):
return (fac[n]*(finv[k]*finv[n-k]%MOD))%MOD
ans = 1
for i in c:
ans *= comb(c[i]+N-1,N-1)
ans %= MOD
print(ans) | p03253 |
#http://nihaoshijie.hatenadiary.jp/entry/2018/02/03/115759
N,M=list(map(int,input().split()))
P=10**9+7
def egcd(a, b):
(x, lastx) = (0, 1)
(y, lasty) = (1, 0)
while b != 0:
q = a // b
(a, b) = (b, a % b)
(x, lastx) = (lastx - q * x, x)
(y, lasty) = (lasty - q * y, y)
return (lastx, lasty, a)
def inv(x):
return egcd(x,P)[0]
Z=2*10**5
Fact=[0 for i in range(Z+1)]
Finv=[0 for i in range(Z+1)]
Fact[0]=1
Finv[0]=1
for i in range(Z):
Fact[i+1]=(Fact[i]*(i+1))%P
Finv[i+1]=inv(Fact[i+1])%P
def C(n,k):
return (Fact[n]*(Finv[k]*Finv[n-k])%P)%P
def factorize(n):
fct = [] # prime factor
b, e = 2, 0 # base, exponent
while b * b <= n:
while n % b == 0:
n = n // b
e = e + 1
if e > 0:
fct.append((b, e))
b, e = b + 1, 0
if n > 1:
fct.append((n, 1))
return fct
D=factorize(M)
ans=1
for seq in D:
k=seq[1]
ans=ans*C(k+N-1,N-1)
ans=ans%P
print(ans)
| import math
N,M=list(map(int,input().split()))
def primecheck(K):
A=int(math.sqrt(K))+1
for i in range(2,A+1):
if K%i==0:
return i
return 1
D=dict()
while(True):
X=int(math.sqrt(M))+1
for i in range(2,X+1):
if M%i==0:
while(True):
if i in D:
D[i]+=1
else:
D[i]=1
M=M//i
if M%i!=0:
break
j=primecheck(M)
if j==1:
if M==1:
break
D[M]=1
break
else:
if j in D:
D[j]=1
else:
D[j]+=1
P=10**9+7
def egcd(a, b):
(x, lastx) = (0, 1)
(y, lasty) = (1, 0)
while b != 0:
q = a // b
(a, b) = (b, a % b)
(x, lastx) = (lastx - q * x, x)
(y, lasty) = (lasty - q * y, y)
return (lastx, lasty, a)
def inv(x):
return egcd(x,P)[0]
Y=2*10**5
Fact=[0 for i in range(Y+1)]
Finv=[0 for i in range(Y+1)]
Fact[0]=1
Finv[0]=1
for i in range(Y):
Fact[i+1]=(Fact[i]*(i+1))%P
Finv[i+1]=inv(Fact[i+1])%P
def C(n,k):
return (Fact[n]*(Finv[k]*Finv[n-k])%P)%P
ans=1
for p in D:
e=D[p]
ans=ans*C(e+N-1,N-1)
ans=ans%P
print(ans)
| p03253 |
import math
N,M=list(map(int,input().split()))
def primecheck(K):
A=int(math.sqrt(K))+1
for i in range(2,A+1):
if K%i==0:
return i
return 1
D=dict()
while(True):
X=int(math.sqrt(M))+1
for i in range(2,X+1):
if M%i==0:
while(True):
if i in D:
D[i]+=1
else:
D[i]=1
M=M//i
if M%i!=0:
break
j=primecheck(M)
if j==1:
if M==1:
break
D[M]=1
break
else:
if j in D:
D[j]=1
else:
D[j]+=1
P=10**9+7
def egcd(a, b):
(x, lastx) = (0, 1)
(y, lasty) = (1, 0)
while b != 0:
q = a // b
(a, b) = (b, a % b)
(x, lastx) = (lastx - q * x, x)
(y, lasty) = (lasty - q * y, y)
return (lastx, lasty, a)
def inv(x):
return egcd(x,P)[0]
Y=2*10**5
Fact=[0 for i in range(Y+1)]
Finv=[0 for i in range(Y+1)]
Fact[0]=1
Finv[0]=1
for i in range(Y):
Fact[i+1]=(Fact[i]*(i+1))%P
Finv[i+1]=inv(Fact[i+1])%P
def C(n,k):
return (Fact[n]*(Finv[k]*Finv[n-k])%P)%P
ans=1
for p in D:
e=D[p]
ans=ans*C(e+N-1,N-1)
ans=ans%P
print(ans)
| import math
N,M=list(map(int,input().split()))
def primecheck(K):
A=int(math.sqrt(K))+1
for i in range(2,A+1):
if K%i==0:
return i
return 1
D=dict()
while(True):
X=int(math.sqrt(M))+1
for i in range(2,X+1):
if M%i==0:
while(True):
if i in D:
D[i]+=1
else:
D[i]=1
M=M//i
if M%i!=0:
break
j=primecheck(M)
if j==1:
if M==1:
break
D[M]=1
break
else:
if j in D:
D[j]=1
else:
D[j]+=1
P=10**9+7
def egcd(a, b):
(x, lastx) = (0, 1)
(y, lasty) = (1, 0)
while b != 0:
q = a // b
(a, b) = (b, a % b)
(x, lastx) = (lastx - q * x, x)
(y, lasty) = (lasty - q * y, y)
return (lastx, lasty, a)
def inv(x):
return egcd(x,P)[0]
Y=N+100
Fact=[0 for i in range(Y+1)]
Finv=[0 for i in range(Y+1)]
Fact[0]=1
Finv[0]=1
for i in range(Y):
Fact[i+1]=(Fact[i]*(i+1))%P
Finv[i+1]=inv(Fact[i+1])%P
def C(n,k):
return (Fact[n]*(Finv[k]*Finv[n-k])%P)%P
ans=1
for p in D:
e=D[p]
ans=ans*C(e+N-1,N-1)
ans=ans%P
print(ans)
| p03253 |
def comb(a, b):
b = min(b, a - b)
res = 1
for i in range(b):
res *= (a - i)
res %= MOD
for div in range(1, b + 1):
res = res * pow(div, MOD - 2, MOD) % MOD
return res
def prime_factorization(x):
res = []
i = 2
left = x + 0
while True:
if (i * i > x) and (left == 1):
break
cnt = 0
while left % i == 0:
left /= i
cnt += 1
if cnt > 0:
res.append(cnt)
# print(i, res)
i += 1
return res
n, m = list(map(int, input().split()))
MOD = 10 ** 9 + 7
ans = 1
for power in prime_factorization(m):
ans *= comb(n - 1 + power, power)
ans %= MOD
print(ans) | MOD = 10 ** 9 + 7
def prime_factorization(n):
i = 2
res = []
while i * i <= n:
cnt = 0
while n % i == 0:
n /= i
cnt += 1
if cnt > 0:
res.append(cnt)
i += 1
if n > 1:
res.append(1)
return res
def comb(a, b):
b = min(b, a - b)
if b < 0:
return 0
elif b == 0:
return 1
elif b == 1:
return a
else:
return (a % MOD) * pow(b, MOD - 2, MOD) % MOD * comb(a - 1, b - 1) % MOD
N, M = list(map(int, input().split()))
ans = 1
for power in prime_factorization(M):
ans *= comb(N - 1 + power, power)
ans %= MOD
print(ans) | p03253 |
class Calc:
def __init__(self, max_value, mod):
"""combination(max_value, all)"""
fact = [-1] * (max_value + 1)
fact[0] = 1
fact[1] = 1
for x in range(2, max_value + 1):
fact[x] = x * fact[x - 1] % mod
invs = [1] * (max_value + 1)
invs[max_value] = pow(fact[max_value], mod - 2, mod)
for x in range(max_value - 1, 0, -1):
invs[x] = invs[x + 1] * (x + 1) % mod
self.fact = fact
self.invs = invs
self.mod = mod
def combination(self, n, r):
if n - r < r:
return self.combination(n, n - r)
if r < 0:
return 0
if r == 0:
return 1
if r == 1:
return n
return self.fact[n] * self.invs[r] * self.invs[n - r] % self.mod
def main():
MOD = 10 ** 9 + 7
N, M = list(map(int, input().split()))
def decom(n) -> list:
ret = []
d = 2
cnt = 0
while n % d == 0:
n //= d
cnt += 1
ret.append((d, cnt))
d = 3
while n > 1:
cnt = 0
while n % d == 0:
n //= d
cnt += 1
ret.append((d, cnt))
d += 1
return ret
dlis = decom(M)
cal = Calc(max_value=N + 30, mod=MOD)
ans = 1
for _, cnt in dlis:
ans = (ans * cal.combination(N + cnt - 1, cnt)) % MOD
print(ans)
if __name__ == '__main__':
main()
| class Calc:
def __init__(self, max_value, mod):
"""combination(max_value, all)"""
fact = [-1] * (max_value + 1)
fact[0] = 1
fact[1] = 1
for x in range(2, max_value + 1):
fact[x] = x * fact[x - 1] % mod
invs = [1] * (max_value + 1)
invs[max_value] = pow(fact[max_value], mod - 2, mod)
for x in range(max_value - 1, 0, -1):
invs[x] = invs[x + 1] * (x + 1) % mod
self.fact = fact
self.invs = invs
self.mod = mod
def combination(self, n, r):
if n - r < r:
return self.combination(n, n - r)
if r < 0:
return 0
if r == 0:
return 1
if r == 1:
return n
return self.fact[n] * self.invs[r] * self.invs[n - r] % self.mod
def main():
MOD = 10 ** 9 + 7
N, M = list(map(int, input().split()))
def decom(n) -> list:
ret = []
d = 2
cnt = 0
while n % d == 0:
n //= d
cnt += 1
ret.append(cnt)
d = 3
while n > 1:
cnt = 0
while n % d == 0:
n //= d
cnt += 1
ret.append(cnt)
d += 2
return ret
dlis = decom(M)
cal = Calc(max_value=N + 30, mod=MOD)
ans = 1
for cnt in dlis:
ans = (ans * cal.combination(N + cnt - 1, cnt)) % MOD
print(ans)
if __name__ == '__main__':
main()
| p03253 |
class Calc:
def __init__(self, max_value, mod):
"""combination(max_value, all)"""
fact = [-1] * (max_value + 1)
fact[0] = 1
fact[1] = 1
for x in range(2, max_value + 1):
fact[x] = x * fact[x - 1] % mod
invs = [1] * (max_value + 1)
invs[max_value] = pow(fact[max_value], mod - 2, mod)
for x in range(max_value - 1, 0, -1):
invs[x] = invs[x + 1] * (x + 1) % mod
self.fact = fact
self.invs = invs
self.mod = mod
def combination(self, n, r):
if n - r < r:
return self.combination(n, n - r)
if r < 0:
return 0
if r == 0:
return 1
if r == 1:
return n
return self.fact[n] * self.invs[r] * self.invs[n - r] % self.mod
def gen(n):
x = n
d = 2
cnt = 0
while x % d == 0:
x //= d
cnt += 1
yield cnt
d = 3
ma = d * d
while ma <= n:
cnt = 0
while x % d == 0:
x //= d
cnt += 1
yield cnt
ma += d * 4 + 4
d += 2
if x > 1:
yield 1
def main():
MOD = 10 ** 9 + 7
N, M = list(map(int, input().split()))
cal = Calc(max_value=N + 30, mod=MOD)
ans = 1
for cnt in gen(M):
ans = (ans * cal.combination(N + cnt - 1, cnt)) % MOD
print(ans)
if __name__ == '__main__':
main()
| def gen(n):
x = n
d = 2
cnt = 0
while x % d == 0:
x //= d
cnt += 1
yield cnt
d = 3
while d * d <= n:
cnt = 0
while x % d == 0:
x //= d
cnt += 1
yield cnt
d += 2
if x > 1:
yield 1
def main():
MOD = 10 ** 9 + 7
N, M = list(map(int, input().split()))
ans = 1
for cnt in gen(M):
for d in range(cnt):
ans = (ans * (N - 1 + cnt - d) % MOD) * pow(d + 1, MOD - 2, MOD) % MOD
print(ans)
if __name__ == '__main__':
main()
| p03253 |
import sys
sys.setrecursionlimit(10 ** 6)
# input = sys.stdin.readline ####
def int1(x): return int(x) - 1
def II(): return int(eval(input()))
def MI(): return list(map(int, input().split()))
def MI1(): return list(map(int1, input().split()))
def LI(): return list(map(int, input().split()))
def LI1(): return list(map(int1, input().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return input().split()
def printlist(lst, k='\n'): print((k.join(list(map(str, lst)))))
INF = float('inf')
from math import ceil, floor, log2
from collections import deque
from itertools import combinations as comb, combinations_with_replacement as comb_w, accumulate, product
from heapq import heapify, heappop, heappush
def prime_factorization(n):
res = []
for i in range(2, int(pow(n, 0.5))+1):
if n % i: continue
ex = 0
while n % i == 0:
n = n // i
ex += 1
res.append((i, ex))
if n != 1:
res.append((n, 1))
return res
def mcomb(n, k, mod):
def mfac(l, r, mod):
ans = l
for i in reversed(list(range(r, l))):
ans *= i
ans %= mod
return ans
A = mfac(n,n-k+1,mod)
B = mfac(k,1,mod)
# B = mpow(B,mod-2,mod)
B = pow(B, mod-2, mod)
return A * B % mod
def solve():
n, m = MI()
fact = prime_factorization(m)
if n == 1:
print((1))
return
# print(fact)
mod = 1000000007
ans = 1
for num, ex in fact:
# print(ex, mcomb(ex+n-2, n-1, mod))
ans *= mcomb(ex+n-1, n-1, mod) % mod
print((ans % mod))
if __name__ == '__main__':
solve()
| import sys
sys.setrecursionlimit(10 ** 9)
# input = sys.stdin.readline ####
def int1(x): return int(x) - 1
def II(): return int(eval(input()))
def MI(): return list(map(int, input().split()))
def MI1(): return list(map(int1, input().split()))
def LI(): return list(map(int, input().split()))
def LI1(): return list(map(int1, input().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def MS(): return input().split()
def LS(): return list(eval(input()))
def LLS(rows_number): return [LS() for _ in range(rows_number)]
def printlist(lst, k=' '): print((k.join(list(map(str, lst)))))
INF = float('inf')
# from math import ceil, floor, log2
# from collections import deque
# from itertools import combinations as comb, combinations_with_replacement as comb_w, accumulate, product, permutations
# from heapq import heapify, heappop, heappush
# import numpy as np
# from numpy import cumsum # accumulate
def prime_factorization(n):
res = []
for i in range(2, int(pow(n, 0.5))+1):
if n % i: continue
ex = 0
while n % i == 0:
n = n // i
ex += 1
res.append((i, ex))
if n != 1:
res.append((n, 1))
return res
def mcomb(n, k, mod):
def mfac(l, r, mod):
ans = l
for i in reversed(list(range(r, l))):
ans *= i
ans %= mod
return ans
A = mfac(n, n-k+1, mod)
B = mfac(k, 1, mod)
# B = mpow(B,mod-2,mod)
B = pow(B, mod-2, mod)
return A * B % mod
def solve():
N, M = MI()
fact = prime_factorization(M)
MOD = 1000000007
if N == 1:
print((1))
return
ans = 1
for num, ex in fact:
ans = ans * mcomb(ex+N-1, N-1, MOD)
ans %= MOD
print(ans)
if __name__ == '__main__':
solve()
| p03253 |
class Solution:
def solve(self, N: int, M: int) -> int:
mod = 10**9+7
INT_MAX = 10**7
# calculate {m+n}C{n}
def egcd(a, b):
if a == 0:
return b, 0, 1
else:
g, y, x = egcd(b % a, a)
return g, x - (b // a) * y, y
def modinv(a, m):
g, x, y = egcd(a, m)
if g != 1:
raise Exception('modular inverse does not exist')
else:
return x % m
def combination(n: int, r: int, mod: int = 10**9+7) -> int:
r = min(r, n-r)
res = 1
for i in range(r):
res = res * (n-i) * modinv(i+1, mod) % mod
return res
# prime list
isPrime = [True] * (INT_MAX + 1)
isPrime[0], isPrime[1] = False, False
primes = []
for i in range(2, len(isPrime)):
if isPrime[i] == True:
primes.append(i)
for j in range(2 * i, len(isPrime), i):
isPrime[j] = False
# solve
m = M
answer = 1
factors = {}
while m > 1:
for p in primes:
factors[p] = 0
while m % p == 0:
m //= p
factors[p] += 1
if factors[p] > 0:
answer *= combination(N + factors[p] - 1, N - 1, mod=mod)
answer %= mod
return answer
if __name__ == '__main__':
# standard input
N, M = list(map(int, input().split()))
# solve
solution = Solution()
print((solution.solve(N, M)))
| import math
class Solution:
def solve(self, N: int, M: int) -> int:
mod = 10**9+7
INT_MAX = 10**9
# calculate {m+n}C{n}
def egcd(a, b):
if a == 0:
return b, 0, 1
else:
g, y, x = egcd(b % a, a)
return g, x - (b // a) * y, y
def modinv(a, m):
g, x, y = egcd(a, m)
if g != 1:
raise Exception('modular inverse does not exist')
else:
return x % m
def combination(n: int, r: int, mod: int = 10**9+7) -> int:
r = min(r, n-r)
res = 1
for i in range(r):
res = res * (n-i) * modinv(i+1, mod) % mod
return res
# solve
m = M
answer = 1
factors = {}
for i in range(2, int(math.sqrt(M))+1):
factor = 0
while m % i == 0:
m //= i
factor += 1
if factor > 0:
answer *= combination(N + factor - 1, N - 1, mod=mod)
answer %= mod
if m > 1:
answer *= N
answer %= mod
return answer
if __name__ == '__main__':
# standard input
N, M = list(map(int, input().split()))
# solve
solution = Solution()
print((solution.solve(N, M)))
| p03253 |
import collections,math,sys
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
N,M = LI()
ans = 1
def prime_factor(num):
prime_factor = collections.defaultdict(int)
for i in range(2,int(num**0.5)+1):
while num%i==0:
prime_factor[i] += 1
num //= i
if num>1:
prime_factor[num]=1
return prime_factor
for v in list(prime_factor(M).values()):
ans *= math.factorial(v+N-1)//math.factorial(v)//math.factorial(N-1)
ans %= 10**9+7
print(ans) | import collections,sys
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
N,M = LI()
ans = 1
def prime_factor(num):
prime_factor = collections.defaultdict(int)
for i in range(2,int(num**0.5)+1):
while num%i==0:
prime_factor[i] += 1
num //= i
if num>1:
prime_factor[num]=1
return prime_factor
def nCr(n,r,mod):
comb_count = 1
for i in range(r):
comb_count *= n-i
comb_count %= mod
for j in range(1,r+1):
comb_count *= pow(j,mod-2,mod)
comb_count %= mod
return comb_count
for v in list(prime_factor(M).values()):
ans *= nCr(v+N-1,v,10**9+7)
ans %= 10**9+7
print(ans)
| p03253 |
# -*- coding: utf-8 -*-
"""
参考：http://drken1215.hatenablog.com/entry/2018/09/23/224100
http://tutuz.hateblo.jp/entry/2018/09/24/121248
・素因数分解と重複組み合わせ
・毎回階乗やると死ぬから階乗と逆元のテーブル作る(忘れてた)
"""
from collections import defaultdict
from math import sqrt
MOD = 10 ** 9 + 7
def fact_prime(num):
d = defaultdict(int)
# 終点はルート切り捨て+1
end = int(sqrt(num)) + 1
for i in range(2, end+1):
cnt = 0
# 素因数分解：小さい方から割れるだけ割って素数をカウント
while num % i == 0:
num //= i
d[i] += 1
# 1まで来たら終了
if num == 1:
break
# 最後までそのまま来たやつはnumが素数(ただし1^1は1^0なので数に入れない)
if num != 1:
d[num] += 1
return d
# とりあえずv+N-1が収まればいいはず
MAX = 10 ** 5 * 2
# 予め組み合わせ計算に必要な階乗と逆元のテーブルを作っておく
factorial = [1] * (MAX)
factorial[0] = factorial[1] = 1
for i in range(2, MAX):
factorial[i] = factorial[i-1] * i % MOD
inverse = [1] * (MAX)
# powに第三引数入れると冪乗のmod付計算を高速にやってくれる
inverse[MAX-1] = pow(factorial[MAX-1], MOD-2, MOD)
for i in range(MAX-2, 0, -1):
# 最後から戻っていくこのループならH+W回powするより処理が速い
inverse[i] = inverse[i+1] * (i+1) % MOD
# 組み合わせの数
def nCr(n, r):
# 10C7 = 10C3
r = min(r, n-r)
# 分子の計算
numerator = factorial[n]
# 分母の計算
denominator = inverse[r] * inverse[n-r] % MOD
return numerator * denominator % MOD
N, M = list(map(int, input().split()))
# d = fact_prime(M)
# print(d)
ans = 1
for k, v in list(fact_prime(M).items()):
# 重複組み合わせ
# v個のkとN-1個の仕切りから、v個を並べる(v+N-1個のマスからv個を選び出す組み合わせ)
ans = (ans * nCr(v+N-1, v)) % MOD
print(ans)
| # -*- coding: utf-8 -*-
import sys
def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(eval(input()))
def MAP(): return list(map(int, input().split()))
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
MOD = 10 ** 9 + 7
def factorize(num: int) -> dict:
""" 素因数分解 """
from math import sqrt
from collections import Counter
d = Counter()
# 終点はルート切り捨て+1
for i in range(2, int(sqrt(num))+1):
# 素因数分解：小さい方から割れるだけ割って素数をカウント
while num % i == 0:
num //= i
d[i] += 1
# 1まで分解したら終了
if num == 1:
break
# 最後に残ったnumは素数(ただし1^1は1^0なので数に入れない)
if num != 1:
d[num] += 1
return d
class FactInvMOD:
""" 階乗たくさん使う時用のテーブル準備 """
def __init__(self, MAX, MOD):
""" MAX：階乗に使う数値の最大以上まで作る """
MAX += 1
self.MAX = MAX
self.MOD = MOD
# 階乗テーブル
factorial = [1] * MAX
factorial[0] = factorial[1] = 1
for i in range(2, MAX):
factorial[i] = factorial[i-1] * i % MOD
# 階乗の逆元テーブル
inverse = [1] * MAX
# powに第三引数入れると冪乗のmod付計算を高速にやってくれる
inverse[MAX-1] = pow(factorial[MAX-1], MOD-2, MOD)
for i in range(MAX-2, 0, -1):
# 最後から戻っていくこのループならMAX回powするより処理が速い
inverse[i] = inverse[i+1] * (i+1) % MOD
self.fact = factorial
self.inv = inverse
def nCr(self, n, r):
""" 組み合わせの数 (必要な階乗と逆元のテーブルを事前に作っておく) """
if n < r: return 0
# 10C7 = 10C3
r = min(r, n-r)
# 分子の計算
numerator = self.fact[n]
# 分母の計算
denominator = self.inv[r] * self.inv[n-r] % self.MOD
return numerator * denominator % self.MOD
def nPr(self, n, r):
""" 順列 """
if n < r: return 0
return self.fact[n] * self.inv[n-r] % self.MOD
def nHr(self, n, r):
""" 重複組み合わせ """
# r個選ぶところにN-1個の仕切りを入れる
return self.nCr(r+n-1, r)
N, M = MAP()
d = factorize(M)
# 例外処理
if not d:
print((1))
exit()
MAX = N + max(d.values())
fim = FactInvMOD(MAX, MOD)
ans = 1
for k, v in list(d.items()):
ans *= fim.nHr(N, v)
ans %= MOD
print(ans)
| p03253 |
#How many ways M=a1*a2*...*aN ex)N=2,M=6 a={1,6},{2,3},{3,2},{6,1}
import math
n,m=list(map(int,input().split()))
factor=[]
c=0
mod=10**9+7
#Prime Factorization [number,times]
while m%2 == 0:
m//=2
c+=1
if c != 0:
factor.append([2,c])
#Alternate
for i in range(3,m+1,2):
c=0
while m%i == 0:
m//=i
c+=1
if c != 0:
#print(i,c)
factor.append([i,c])
if m == 1:
break
if i*i>=m: # m is prime
factor.append([m,1])
break
#print(factor)
def C(n,k):
ans=1
for s in range(1,k+1):
ans*=n
ans//=s
n-=1
return ans
def funcount(length,rest):
a=0
if length==1:
#print(rest)
return 1
elif rest <= 1:
#print("not",rest)
return 0
else:
for i in range(1,rest):
#print(i,end=" ")
a+=funcount(length-1,rest-i)
return a
way=1
for f in factor:
sum=0
for k in range(1,f[1]+1):
sum+=funcount(k,f[1])*C(n,k)
way=(way*sum)%mod
print((way%mod)) | #How many ways M=a1*a2*...*aN ex)N=2,M=6 a={1,6},{2,3},{3,2},{6,1}
import math
n,m=list(map(int,input().split()))
factor=[]
c=0
mod=10**9+7
#Prime Factorization [number,times]
while m%2 == 0:
m//=2
c+=1
'''
if c>=20:
c=0
break
'''
if c != 0:
factor.append([2,c])
#Alternate
for i in range(3,m+1,2):
c=0
while m%i == 0:
m//=i
c+=1
if c != 0:
#print(i,c)
factor.append([i,c])
if m == 1:
break
if i*i>=m: # m is prime
factor.append([m,1])
break
#print(factor)
def C(n,k):
ans=1
for s in range(1,k+1):
ans*=n
ans//=s
n-=1
return ans
def funcount(length,rest,memo):
a=0
if length==1:
#print(length,rest)
memo[length][rest]=1
return 1,memo
elif rest <= 1:
#print(length,rest)
memo[length][rest]=0
return 0,memo
if memo[length][rest] != -1:
return memo[length][rest],memo
else:
for i in range(1,rest):
#print(i,end=" ")
a+=funcount(length-1,rest-i,memo)[0]
memo=funcount(length-1,rest-i,memo)[1]
#print(memo)
memo[length][rest]=a
return a,memo
way=1
for f in factor:
sum=0
for k in range(1,f[1]+1):
memo=[[-1 for r in range(f[1]+1)] for l in range(k+1)]
#print(memo)
sum+=funcount(k,f[1],memo)[0]*C(n,k)
way=(way*sum)%mod
print((way%mod)) | p03253 |
from math import factorial
from collections import Counter
N, M = list(map(int, input().split()))
MOD = 10 ** 9 + 7
def prime_factorize(n):
a = []
while n % 2 == 0:
a.append(2)
n //= 2
f = 3
while f * f <= n:
if n % f == 0:
a.append(f)
n //= f
else:
f += 2
if n != 1:
a.append(n)
return a
A = prime_factorize(M)
c = Counter(A)
cases = 1
for v in list(c.values()):
if v > 1:
x = factorial(v+N-1)%MOD*pow(factorial(N-1)*factorial(v) % MOD, MOD-2, MOD)%MOD
cases *= x
else:
cases *= N
cases %= MOD
print(cases)
| import sys
from collections import Counter
sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))
N, M = lr()
MOD = 10 ** 9 + 7
def prime_factorize(n): # Nの素因数分解
a = []
while n % 2 == 0:
a.append(2)
n //= 2
f = 3
while f * f <= n:
if n % f == 0:
a.append(f)
n //= f
else:
f += 2
if n != 1:
a.append(n)
return a
def combination(n, x, mod=10**9+7):
# nCx 組み合わせ ex) combination(5, 2) = 10
factorial = [1] * (n+1)
t = 1
for i in range(1, n+1):
t = (t * i) % mod
factorial[i] = t
tmp = factorial[n]
tmp = (tmp * pow(factorial[x], mod-2, mod)) % mod
tmp = (tmp * pow(factorial[n-x], mod-2, mod)) % mod
return tmp
A = prime_factorize(M)
counter = Counter(A)
answer = 1
for c in list(counter.values()):
answer *= combination((N-1+c), c)
answer %= MOD
print(answer)
# 19 | p03253 |
N, M = [int(i) for i in input().split()]
def prime_decomposition(n):
i = 2
table = []
while i * i <= n:
while n % i == 0:
n //= i
table.append(i)
i += 1
if n > 1:
table.append(n)
return table
def cmb(n, r):
N, R = n, r
for i in range(1, r):
N *= n - i
R *= r - i
return N // R
from collections import Counter
A = Counter(prime_decomposition(M))
mod = 10 ** 9 + 7
result = 1
for a in list(A.values()):
result = result * cmb(a + N - 1, a) % mod
print(result) | N, M = [int(i) for i in input().split()]
def prime_decomposition(n):
table = []
i = 2
while i * i <= n:
count = 0
while n % i == 0:
n //= i
count += 1
if count != 0:
table.append((i, count))
i += 1
if n > 1:
table.append((n, 1))
return table
def cmb(n, r):
N, R = n, r
for i in range(1, r):
N *= n - i
R *= r - i
return N // R
mod = 10 ** 9 + 7
A = prime_decomposition(M)
result = 1
for _, a in A:
result = result * cmb(a + N - 1, a) % mod
print(result) | p03253 |
import math
import sys
import bisect
import itertools
N, M = [int(x) for x in input().split()]
MOD = 10 ** 9 + 7
divisor = []
dict = {}
m = M
d = 2
while m != 1:
while m % d == 0:
# divisor.append(d)
m //= d
dict[d] = dict.get(d, 0) + 1
d += 1
C = list(dict.values())
ret = 1
# def combinations_count(n, r):
# return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def combinations_count(n, r):
a = max(r, n-r)
b = min(r, n-r)
r = 1
for i in range(a+1, n+1):
r *= i
return r // math.factorial(b)
for c in C:
ret *= combinations_count(c + N - 1, c)
ret %= MOD
print(ret)
| import math
N, M = [int(x) for x in input().split()]
MOD = 10 ** 9 + 7
divisor = []
dict = {}
m = M
d = 2
while m != 1:
while m % d == 0:
# divisor.append(d)
m //= d
dict[d] = dict.get(d, 0) + 1
d += 1
C = list(dict.values())
ret = 1
# def combinations_count(n, r):
# return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def combinations_count(n, r):
a = max(r, n-r)
b = min(r, n-r)
r = 1
for i in range(a+1, n+1):
r *= i
return r // math.factorial(b)
for c in C:
ret *= combinations_count(c + N - 1, c)
ret %= MOD
print(ret)
| p03253 |
import math
N, M = [int(x) for x in input().split()]
MOD = 10 ** 9 + 7
divisor = []
dict = {}
m = M
d = 2
while m != 1:
while m % d == 0:
# divisor.append(d)
m //= d
dict[d] = dict.get(d, 0) + 1
d += 1
C = list(dict.values())
ret = 1
# def combinations_count(n, r):
# return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def combinations_count(n, r):
a = max(r, n-r)
b = min(r, n-r)
r = 1
for i in range(a+1, n+1):
r *= i
return r // math.factorial(b)
for c in C:
ret *= combinations_count(c + N - 1, c)
ret %= MOD
print(ret)
| import math
N, M = [int(x) for x in input().split()]
MOD = 10 ** 9 + 7
divisor = []
dict = {}
m = M
d = 2
while d*d <= m:
while m % d == 0:
m //= d
dict[d] = dict.get(d, 0) + 1
d += 1
if m > 1:
dict[d] = dict.get(m, 0) + 1
C = list(dict.values())
ret = 1
# def combinations_count(n, r):
# return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def combinations_count(n, r):
a = max(r, n-r)
b = min(r, n-r)
r = 1
for i in range(a+1, n+1):
r *= i
return r // math.factorial(b)
for c in C:
ret *= combinations_count(c + N - 1, c)
ret %= MOD
print(ret)
| p03253 |
import math
N, M = list(map(int, input().split()))
max = int(math.sqrt(M))
mod = 7 + 10**9
F = []
def Prime(i): #素数であればTrueを返す
root = math.sqrt(i)
j, div = 2, False
while j <= root:
if i % j == 0:
div = True
break
j += 1
return (True if not div else False)
def comb(n, r):
ans = math.factorial(n) // (math.factorial(n-r) * math.factorial(r))
return ans % mod
ans = 1
for i in range(2, max + 1):
if M % i == 0:
div = M // i
if Prime(i):
pow = 0
while M % (i ** (pow+1)) == 0:
pow += 1
ans *= comb(pow + N -1, pow)
ans %= mod
if Prime(div):
pow = 0
while M % (i ** (pow+1)) == 0:
pow += 1
ans *= comb(pow + N - 1, pow)
ans %= mod
print(ans) | import math
def InvMod(i, pow, mod): #階乗のmodを計算
if pow == 1:
return i % mod
else:
if pow % 2 == 0:
return InvMod((i**2) % mod, pow//2, mod) % mod
else:
return InvMod((i**2) % mod, pow//2, mod) * i % mod
def Prime(i): #素数であればTrueを返す
root = math.sqrt(i)
j, div = 2, True
while j <= root:
if i % j == 0:
div = False
break
j += 1
return div
N, M = list(map(int, input().split()))
max = int(math.sqrt(M))
mod = 7 + 10**9
Pinv = [0]
Pfact = 1
for i in range(1, 31): #(階乗)^-1の計算, 2^31 > 10^9なので階乗は高々30乗まで
Pfact *= i
Pfact %= mod
Pinv.append(InvMod(Pfact, mod-2, mod))
P = []
for i in range(2, max+1): #素因数の列挙
if M % i == 0:
if Prime(i):
P.append(i)
if Prime(M//i) and i**2 != M:
P.append(M//i)
ans = 1
for p in P:
C, pow = M, 0
while C % p == 0:
pow += 1
C //= p
comb = Pinv[pow] #(N-1)!/pow!(N-1)!
for i in range(pow): #comb * (N-1+1)(N-1+2)…(N-1+pow)
comb *= (N+i)
comb %= mod
ans *= comb
ans %= mod
print(ans) | p03253 |
from collections import Counter
import math
N,M = list(map(int,input().split()))
nf = math.factorial(N)
# 因数分解
def prime_factorize(n):
a = []
while n % 2 == 0:
a.append(2)
n //= 2
f = 3
while f * f <= n:
if n % f == 0:
a.append(f)
n //= f
else:
f += 2
if n != 1:
a.append(n)
return a
a = prime_factorize(M)
c = Counter(a)
l = []
for i in list(c.values()):
# 階乗
# 重複組み合わせ
l.append(math.factorial(N+i-1)//(math.factorial(N-1)*math.factorial(i)))
ans = 1
for i in l:
ans *= i
print((ans%(10**9+7))) | from collections import Counter
import math
mod = 10**9+7
N,M = list(map(int,input().split()))
factors = []
f = 2
while M%f==0:
M//=2
factors.append(f)
f = 3
while f*f<=M:
if M%f==0:
M//=f
factors.append(f)
else:
f+=2
if M!=1:
factors.append(M)
count = Counter(factors)
def choose(n,k):
return math.factorial(n)//(math.factorial(n-k)*math.factorial(k))
ans = 1
for v in list(count.values()):
ans *= choose(N+v-1,N-1)
ans %= mod
print(ans) | p03253 |
from math import factorial
def H(x, y):
return factorial(x + y - 1) // (factorial(x - 1) * factorial(y))
n, m = list(map(int, input().split()))
p = 2
prime_factorization = []
while p * p <= m:
count = 0
while m % p == 0:
m //= p
count += 1
if count > 0:
prime_factorization.append(count)
p += 1
if m > 1:
prime_factorization.append(1)
ans = 1
for r in prime_factorization:
ans *= H(n, r)
print((ans % 1000000007)) | def C(x, y):
z = 1
for i in range(x, x-y, -1):
z *= i
for i in range(y, 1, -1):
z //= i
return z
def H(x, y):
return C(x+y-1, y)
n, m = list(map(int, input().split()))
p = 2
prime_factorization = []
while p * p <= m:
count = 0
while m % p == 0:
m //= p
count += 1
if count > 0:
prime_factorization.append(count)
p += 1
if m > 1:
prime_factorization.append(1)
ans = 1
for r in prime_factorization:
ans *= H(n, r)
print((ans % 1000000007)) | p03253 |
# -*- coding: utf-8 -*-
from collections import defaultdict
# mod mでの二項係数を求める
class BiCoeff(object):
def __init__(self, MAX, m):
super(BiCoeff, self).__init__()
fac = [0]*MAX
finv = [0]*MAX
inv = [0]*MAX
fac[0] = 1
fac[1] = 1
finv[0] = 1
finv[1] = 1
inv[1] = 1
for i in range(2,MAX):
fac[i] = (fac[i-1]*i)%m
inv[i] = m - (inv[m%i] * (m//i))%m
finv[i] = (finv[i-1] * inv[i])%m
self.MAX = MAX
self.m = m
self.fac = fac
self.finv = finv
self.inv = inv
def calc(self,n,k):
if n<k:
return 0
if n<0 or k<0:
return 0
return (self.fac[n] * (self.finv[k]*self.finv[n-k])%self.m)%self.m
MOD = 10**9+7
n, m = list(map(int, input().split()))
pl = defaultdict(int)
x = m
p = 2
while p*p<x+10:
while x%p==0:
pl[p] += 1
x //= p
p += 1
if x>1:
pl[x] += 1
coeff = BiCoeff(10**6, MOD)
res = 1
for k in pl:
res *= coeff.calc(n+pl[k]-1, pl[k])
res %= MOD
print(res)
| # -*- coding: utf-8 -*-
def primeFactors(n):
res = []
while n%2==0:
res.append(2)
n //= 2
x = 3
while n>1 and n>=x*x:
while n%x==0:
res.append(x)
n //= x
x += 2
if n>1:
res.append(n)
return res
class BiCoeff(object):
def __init__(self, MAX, m):
super(BiCoeff, self).__init__()
fac = [0]*MAX
finv = [0]*MAX
inv = [0]*MAX
fac[0] = 1
fac[1] = 1
finv[0] = 1
finv[1] = 1
inv[1] = 1
for i in range(2,MAX):
fac[i] = (fac[i-1]*i)%m
inv[i] = m - (inv[m%i] * (m//i))%m
finv[i] = (finv[i-1] * inv[i])%m
self.MAX = MAX
self.m = m
self.fac = fac
self.finv = finv
self.inv = inv
def calc(self,n,k):
if n<k:
return 0
if n<0 or k<0:
return 0
return (self.fac[n] * (self.finv[k]*self.finv[n-k])%self.m)%self.m
from collections import defaultdict
MOD = 10**9 + 7
n,m = list(map(int, input().split()))
bicoeff = BiCoeff(n+100,MOD)
d = defaultdict(int)
for p in primeFactors(m):
d[p] += 1
res = 1
for v in list(d.values()):
res *= bicoeff.calc(n-1+v,n-1)
res %= MOD
print(res)
| p03253 |
import math
import collections
n, m = list(map(int, input().split()))
factor = []
tmp = int(m ** (1/2)) + 1
for i in range(2, tmp):
while m % i == 0:
m //= i
factor.append(i)
if m > 1:
factor.append(m)
num = list(collections.Counter(factor).most_common())
ans = 1
for x in num:
ans *= (math.factorial(x[1] + n - 1) // (math.factorial(n - 1) * math.factorial(x[1])) % 1000000007)
ans %= 1000000007
print(ans) | import collections
n, m = list(map(int, input().split()))
factor = []
tmp = int(m ** (1/2)) + 1
for i in range(2, tmp):
while m % i == 0:
m //= i
factor.append(i)
if m > 1:
factor.append(m)
num = list(collections.Counter(factor).most_common())
def comb(n, r):
tmp = 1
for i in range(r):
tmp *= n - i
for i in range(r):
tmp //= r - i
return tmp
ans = 1
for x in num:
ans *= (comb(x[1] + n - 1, x[1]) % 1000000007)
ans %= 1000000007
print(ans) | p03253 |
import sys
stdin = sys.stdin
def li(): return list(map(int, stdin.readline().split()))
def li_(): return [int(x)-1 for x in stdin.readline().split()]
def lf(): return list(map(float, stdin.readline().split()))
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())
from bisect import bisect_right
# nの逆元のリスト
def inv_mod(n:int, mod:int) -> list:
inv = [0,1]
for i in range(2,n+1):
inv.append(mod - ((mod//i)*inv[mod%i]) % mod)
return inv
# nの階乗のリスト
def fact(n:int, mod:int) -> list:
fac = [1,1]
res = 1
for i in range(2,n+1):
res = res*i%mod
fac.append(res)
return fac
# nの階乗の逆元のリスト
def fact_inv(n:int, inv:list, mod:int) -> list:
facInv = [1,1]
for i in range(2,n+1):
facInv.append(facInv[i-1]*inv[i] % mod)
return facInv
from collections import Counter
n,m = li()
MOD = 10**9+7
# 二項係数の準備
inv = inv_mod(n,MOD)
fac = fact(n,MOD)
facInv = fact_inv(n,inv,MOD)
# Mの素因数リストを作る
def cd(n:int):
m = 2
cds = set([n])
while m*m <= n:
if n%m == 0:
cds.add(m)
cds.add(n//m)
m += 1
return sorted(list(cds))
cds = cd(m)
memo = []
def dfs(m: int, cds: list, res:int,st:list):
if res == 1:
memo.append(st)
else:
idx = bisect_right(cds,st[-1])
for cdi in cds[:idx]:
if cdi > st[-1]:
pass
else:
if res%cdi == 0:
dfs(m,cds,res//cdi,st+[cdi])
# 辞書順にmを作れるオリジナルなセットを作る
for cdi in cds:
dfs(m,cds,m//cdi,[cdi])
ans = 0
for memoi in memo:
cnt = Counter(memoi)
cnt_v = [ci for ci in list(cnt.values()) if ci > 1]
temp = fac[n]
if len(memoi) <= n:
for cnt_vi in cnt_v:
temp = (temp*facInv[cnt_vi]) % MOD
temp = (temp*facInv[n-len(memoi)]) % MOD
ans = (ans+temp) % MOD
if m==1 or n==1:
print((1))
else:
print((ans%MOD)) | import sys
stdin = sys.stdin
def li(): return list(map(int, stdin.readline().split()))
def li_(): return [int(x)-1 for x in stdin.readline().split()]
def lf(): return list(map(float, stdin.readline().split()))
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())
from collections import Counter
# nの逆元のリスト
def inv_mod(n:int, mod:int) -> list:
inv = [0,1]
for i in range(2,n+1):
inv.append(mod - ((mod//i)*inv[mod%i]) % mod)
return inv
# nの階乗のリスト
def fact(n:int, mod:int) -> list:
fac = [1,1]
res = 1
for i in range(2,n+1):
res = res*i%mod
fac.append(res)
return fac
# nの階乗の逆元のリスト
def fact_inv(n:int, inv:list, mod:int) -> list:
facInv = [1,1]
for i in range(2,n+1):
facInv.append(facInv[i-1]*inv[i] % mod)
return facInv
# 二項係数
def nCr(n:int, r:int, mod:int, fac:list, facInv:list) -> int:
if not (0<=r and r<=n):
return 0
return ((fac[n]*facInv[r]) % mod) * facInv[n-r] % mod
def factorize(n: int):
d = Counter()
m= 2
while m*m <= n:
while n%m == 0:
n //= m
d[m] += 1
m += 1
if n > 1:
d[n] += 1
return d
n,m = li()
MOD = 10**9+7
# 二項係数の準備
inv = inv_mod(n+100,MOD)
fac = fact(n+100,MOD)
facInv = fact_inv(n+100,inv,MOD)
primes = factorize(m)
ans = 1
if n == 1 or m == 1:
print(ans)
else:
for pi in list(primes.values()):
ans = ans * nCr(n+pi-1, pi, MOD, fac, facInv) % MOD
print(ans)
| p03253 |
import sys
stdin = sys.stdin
sys.setrecursionlimit(10**5)
def li(): return list(map(int, stdin.readline().split()))
def li_(): return [int(x)-1 for x in stdin.readline().split()]
def lf(): return list(map(float, stdin.readline().split()))
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())
from collections import Counter
def factorize(n: int):
d = Counter()
m= 2
while m*m <= n:
while n%m == 0:
n //= m
d[m] += 1
m += 1
if n > 1:
d[n] += 1
return d
# nの逆元のリスト
def inv_mod(n:int, mod:int) -> list:
inv = [0,1]
for i in range(2,n+1):
inv.append(mod - ((mod//i)*inv[mod%i]) % mod)
return inv
# nの階乗のリスト
def fact(n:int, mod:int) -> list:
fac = [1,1]
res = 1
for i in range(2,n+1):
res = res*i%mod
fac.append(res)
return fac
# nの階乗の逆元のリスト
def fact_inv(n:int, inv:list, mod:int) -> list:
facInv = [1,1]
for i in range(2,n+1):
facInv.append(facInv[i-1]*inv[i] % mod)
return facInv
# 二項係数
def nCr(n:int, r:int, mod:int, fac:list, facInv:list) -> int:
if not (0<=r and r<=n):
return 0
return ((fac[n]*facInv[r]) % mod) * facInv[n-r] % mod
# 重複組み合わせ
def nHr(n:int, r:int, mod:int, fac:list, facInv:list) -> int:
if r<0 or n<0:
return 0
else:
return nCr(n+r-1,r,mod,fac,facInv)
n,m = li()
MOD = 10**9+7
inv = inv_mod(2*10**5, MOD)
fac = fact(2*10**5, MOD)
facinv = fact_inv(2*10**5,inv,MOD)
md = factorize(m)
ans = 1
for k,v in list(md.items()):
ans *= nHr(n,v,MOD,fac,facinv)
ans %= MOD
print(ans)
| import sys
stdin = sys.stdin
sys.setrecursionlimit(10 ** 7)
def li(): return list(map(int, stdin.readline().split()))
def li_(): return [int(x) - 1 for x in stdin.readline().split()]
def lf(): return list(map(float, stdin.readline().split()))
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())
n,m = li()
MOD = 10**9 + 7
from collections import Counter
def factorize(n: int):
d = Counter()
m = 2
while m * m <= n:
while n % m == 0:
n //= m
d[m] += 1
m += 1
if n > 1:
d[n] += 1
return d
# nの逆元のリスト
def inv_mod(n:int, mod:int) -> list:
inv = [0,1]
for i in range(2,n+1):
inv.append(mod - ((mod//i)*inv[mod%i]) % mod)
return inv
# nの階乗のリスト
def fact(n: int, mod: int) -> list:
fac = [1, 1]
res = 1
for i in range(2, n + 1):
res = res * i % mod
fac.append(res)
return fac
# nの階乗の逆元のリスト
def fact_inv(n: int, inv: list, mod: int) -> list:
facInv = [1, 1]
for i in range(2, n + 1):
facInv.append(facInv[i - 1] * inv[i] % mod)
return facInv
# 二項係数
def nCr(n: int, r: int, mod: int, fac: list, facInv: list) -> int:
if not (0 <= r and r <= n):
return 0
return ((fac[n] * facInv[r]) % mod) * facInv[n - r] % mod
inv = inv_mod(n+100, MOD)
fac = fact(n+100, MOD)
fac_inv = fact_inv(n+100, inv, MOD)
divs = factorize(m)
ans = 1
for _, vals in list(divs.items()):
ans *= nCr(vals+n-1, vals, MOD, fac, fac_inv)
ans %= MOD
print(ans) | p03253 |
import math
import sys
import collections
mod = 1000000007
sys.setrecursionlimit(mod)
fact = {1: 1}
def run(n, m):
# print('{}を{}個の数列で表現'.format(m, n))
ans = 1
primes = []
for i in range(2, m):
if m == 1:
break
if i*i > m:
break
if m % i == 0:
cnt = 0
while m % i == 0:
cnt += 1
m //= i
primes.append(i)
ans *= comb(cnt+n-1, n-1)
ans %= mod
# counts = collections.Counter(primes)
# print(counts)
# for (_, v) in counts.items():
# ans *= comb(v+n-1, n-1)
# ans %= mod
if m != 1:
ans *= n
ans %= mod
return ans
def comb(n, r):
mul = math.factorial(n) // math.factorial(n - r)
div = math.factorial(r)
# mul = factorial(n) // factorial(n - r)
# div = factorial(r)
mul %= mod
div %= mod
return (mul * modpow(div, (mod-2))) % mod
'''
def factorial(n):
if n in fact:
return fact[n]
else:
fact[n] = n*factorial(n-1)
return fact[n]
'''
def modpow(a, p):
if p == 0:
return 1
if p % 2 == 0:
halfp = p // 2
half = modpow(a, halfp)
return int((half * half) % mod)
else:
return int((a * modpow(a, p-1)) % mod)
def main():
n, m = list(map(int, input().split()))
print((run(n, m)))
if __name__ == '__main__':
main()
| import math
import sys
import collections
mod = 1000000007
sys.setrecursionlimit(mod)
fact = {1: 1}
def run(n, m):
# print('{}を{}個の数列で表現'.format(m, n))
ans = 1
primes = []
for i in range(2, m):
if m == 1:
break
if i*i > m:
break
if m % i == 0:
cnt = 0
while m % i == 0:
cnt += 1
m //= i
primes.append(i)
ans *= comb(cnt+n-1, n-1)
ans %= mod
# counts = collections.Counter(primes)
# print(counts)
# for (_, v) in counts.items():
# ans *= comb(v+n-1, n-1)
# ans %= mod
if m != 1:
ans *= n
ans %= mod
return ans
def comb(n, r):
if r > (n-r):
r = n-r
mul = 1
div = 1
for i in range(r):
mul *= n-i
div *= i+1
mul %= mod
div %= mod
# mul = math.factorial(n) // math.factorial(n - r)
# div = math.factorial(r)
# mul = factorial(n) // factorial(n - r)
# div = factorial(r)
mul %= mod
div %= mod
return (mul * modpow(div, (mod-2))) % mod
'''
def factorial(n):
if n in fact:
return fact[n]
else:
fact[n] = n*factorial(n-1)
return fact[n]
'''
def modpow(a, p):
if p == 0:
return 1
if p % 2 == 0:
halfp = p // 2
half = modpow(a, halfp)
return int((half * half) % mod)
else:
return int((a * modpow(a, p-1)) % mod)
def main():
n, m = list(map(int, input().split()))
print((run(n, m)))
if __name__ == '__main__':
main()
| p03253 |
import math
mod = 1000000007
N,M = list(map(int,input().strip().split()))
m_sqrt = int(math.sqrt(M))
def P(n, r):
return math.factorial(n)//math.factorial(n-r)
def C(n, r):
return P(n, r)//math.factorial(r)
ans = 1
cnt = 0
while M%2 == 0:
M = M//2
cnt += 1
ans *= C(N+cnt-1,cnt)
cnt = 0
for i in range(3,m_sqrt+1,2):
while M%i == 0:
M = M//i
cnt += 1
if cnt != 0:
ans *= C(N+cnt-1,cnt)
cnt = 0
if M != 1:
ans *= C(N,1)
print((ans%mod))
| import math
mod = 1000000007
N,M = list(map(int,input().strip().split()))
l = []
def P(n, r):
return math.factorial(n)//math.factorial(n-r)
def C(n, r):
return P(n, r)//math.factorial(r)
ans = 1
cnt = 0
while M%2 == 0:
M //= 2
cnt += 1
l.append(cnt)
cnt = 0
i = 3
while i**2 <= M:
cnt = 0
while M%i == 0:
M //= i
cnt += 1
if cnt != 0:
l.append(cnt)
cnt = 0
i += 2
if M != 1:
l.append(1)
for i in l:
for j in range(i):
ans = ans*(N+j)//(j+1)
print((ans%mod))
| p03253 |
import sys
read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
MOD = 10**9+7
fac = [1, 1] # 元テーブル
f_inv = [1, 1] # 逆元テーブル
inv = [0, 1] # 逆元テーブル計算用テーブル
def prepare(n, mod):
for i in range(2, n+1):
fac.append((fac[-1] * i) % mod)
inv.append((-inv[mod % i] * (mod//i)) % mod)
f_inv.append((f_inv[-1] * inv[-1]) % mod)
def cmb(n, r, mod):
if n < 0 or r < 0:
return 0
if r > n:
return 0
return fac[n] * f_inv[r] * f_inv[n-r] % mod
def prime_factorization(n):
d = []
i, e = 2, 0 # factor, exponent
while i * i <= n:
while n % i == 0:
n //= i
e += 1
if e > 0:
d.append((i, e))
i += 1
e = 0
if n > 1:
d.append((n, 1))
return d
def main():
N,M = list(map(int, readline().split()))
prepare(N+100, MOD)
d = prime_factorization(M)
ans = 1
for i, e in d:
ans *= cmb(N-1+e, e, MOD)
ans %= MOD
print(ans)
if __name__ == "__main__":
main()
| import sys
read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
MOD = 10**9+7
fac = [1, 1] # 元テーブル
f_inv = [1, 1] # 逆元テーブル
inv = [0, 1] # 逆元テーブル計算用テーブル
def prepare(n, mod):
for i in range(2, n+1):
fac.append((fac[-1] * i) % mod)
def cmb(n, r, mod):
if n < 0 or r < 0:
return 0
if r > n:
return 0
return fac[n] * pow(fac[r],MOD-2,MOD) * pow(fac[n-r],MOD-2,MOD) % mod
def prime_factorization(n):
d = []
i, e = 2, 0 # factor, exponent
while i * i <= n:
while n % i == 0:
n //= i
e += 1
if e > 0:
d.append((i, e))
i += 1
e = 0
if n > 1:
d.append((n, 1))
return d
def main():
N,M = list(map(int, readline().split()))
prepare(N+100, MOD)
d = prime_factorization(M)
ans = 1
for i, e in d:
ans *= cmb(N-1+e, e, MOD)
ans %= MOD
print(ans)
if __name__ == "__main__":
main()
| p03253 |
import sys
read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
MOD = 10**9+7
fac = [1, 1] # 元テーブル
f_inv = [1, 1] # 逆元テーブル
inv = [0, 1] # 逆元テーブル計算用テーブル
def prepare(n, mod):
for i in range(2, n+1):
fac.append((fac[-1] * i) % mod)
def cmb(n, r, mod):
if n < 0 or r < 0:
return 0
if r > n:
return 0
return fac[n] * pow(fac[r],MOD-2,MOD) * pow(fac[n-r],MOD-2,MOD) % mod
def prime_factorization(n):
d = []
i, e = 2, 0 # factor, exponent
while i * i <= n:
while n % i == 0:
n //= i
e += 1
if e > 0:
d.append((i, e))
i += 1
e = 0
if n > 1:
d.append((n, 1))
return d
def main():
N,M = list(map(int, readline().split()))
prepare(N+100, MOD)
d = prime_factorization(M)
ans = 1
for i, e in d:
ans *= cmb(N-1+e, e, MOD)
ans %= MOD
print(ans)
if __name__ == "__main__":
main()
| # AC: msec(Python3)
from math import factorial
import sys
read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
MOD = 10**9+7
def cmb(n, r):
if n < 0 or r < 0:
return 0
if r > n:
return 0
r = min(n-r, r)
res = 1
for i in range(r):
res *= n - i
return res // factorial(r)
def prime_factorization(n):
d = []
i, e = 2, 0 # factor, exponent
while i * i <= n:
while n % i == 0:
n //= i
e += 1
if e > 0:
d.append((i, e))
i += 1
e = 0
if n > 1:
d.append((n, 1))
return d
def main():
N,M = list(map(int, readline().split()))
d = prime_factorization(M)
ans = 1
for i, e in d:
ans *= cmb(N-1+e, e)
ans %= MOD
print(ans)
if __name__ == "__main__":
main()
| p03253 |
from math import factorial
def pff(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 comb(n, r):
return factorial(n) // (factorial(n - r) * factorial(r))
N, M = list(map(int, input().split()))
L = pff(M)
anst = int(1)
for i in list(L.values()):
anst *= comb(i+N-1, i)
anst = anst%1000000007
ans = anst
print(ans) | from math import factorial
from operator import mul
from functools import reduce
def comb2(n,r):
r = min(n - r, r)
if r == 0: return 1
over = reduce(mul, list(range(n, n - r, -1)))
under = reduce(mul, list(range(1, r + 1)))
return over // under
def pff(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
N, M = list(map(int, input().split()))
L = pff(M)
anst = int(1)
for i in list(L.values()):
anst *= comb2(i+N-1, i)
anst = anst%1000000007
ans = anst
print(ans) | p03253 |
import math
def main():
N,M = list(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() | import sys
input = sys.stdin.buffer.readline
from collections import defaultdict
import copy
def main():
N,M = list(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() | p03253 |
import sys
input = sys.stdin.buffer.readline
from collections import defaultdict
import copy
def main():
N,M = list(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() | import sys
input = sys.stdin.buffer.readline
def main():
N,M = list(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])
return arr
cl = factorization(M)
def combinations(x,y,N):
fac = [0]*(N+1)
fac[0],fac[1] = 1,1
for i in range(2,N+1):
fac[i] = (fac[i-1]*i)%MOD
return (fac[x+y]*pow(fac[x],MOD-2,MOD)*pow(fac[y],MOD-2,MOD))%MOD
ans = 1
for pr,num in cl:
ans *= combinations(N-1,num,N+num)
ans %= MOD
print(ans)
if __name__ == "__main__":
main()
| p03253 |
import sys
input = sys.stdin.buffer.readline
def main():
K,M = list(map(int,input().split()))
def factorize(n):
fct = [] # prime factor
b, e = 2, 0 # base, exponent
while b * b <= n:
while n % b == 0:
n = n // b
e = e + 1
if e > 0:
fct.append((b, e))
b, e = b + 1, 0
if n > 1:
fct.append((n, 1))
return fct
N = 10**6
MOD = 10**9+7
fac = [0]*(N+1)
fac[0],fac[1] = 1,1
invfac = [0]*(N+1)
invfac[0],invfac[1] = 1,1
for i in range(2,N+1):
fac[i] = (fac[i-1]*i)%MOD
invfac[-1] = pow(fac[-1],MOD-2,MOD)
for i in range(N,0,-1):
invfac[i-1] = (invfac[i]*i)%MOD
def coef(x,y):
num = ((fac[x]*invfac[y])%MOD)*invfac[x-y]%MOD
return num
fl = factorize(M)
ans = 1
for pr,cnt in fl:
ans *= coef(K+cnt-1,K-1)
ans %= MOD
print(ans)
if __name__ == "__main__":
main()
| import sys
input = sys.stdin.buffer.readline
def main():
K,M = list(map(int,input().split()))
def factorize(n):
fct = [] # prime factor
b, e = 2, 0 # base, exponent
while b * b <= n:
while n % b == 0:
n = n // b
e = e + 1
if e > 0:
fct.append((b, e))
b, e = b + 1, 0
if n > 1:
fct.append((n, 1))
return fct
N = 10**5+100
MOD = 10**9+7
fac = [0]*(N+1)
fac[0],fac[1] = 1,1
invfac = [0]*(N+1)
invfac[0],invfac[1] = 1,1
for i in range(2,N+1):
fac[i] = (fac[i-1]*i)%MOD
invfac[-1] = pow(fac[-1],MOD-2,MOD)
for i in range(N,0,-1):
invfac[i-1] = (invfac[i]*i)%MOD
def coef(x,y):
num = ((fac[x]*invfac[y])%MOD)*invfac[x-y]%MOD
return num
fl = factorize(M)
ans = 1
for pr,cnt in fl:
ans *= coef(K+cnt-1,K-1)
ans %= MOD
print(ans)
if __name__ == "__main__":
main()
| p03253 |
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 = list(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))
| 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 = list(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))
| p03253 |
import sys
import math
def input():
return sys.stdin.readline()[:-1]
def combinations_count(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def trial_division(n):
factor = []
tmp = int(math.sqrt(n)) + 1
for num in range(2,tmp):
while n % num == 0:
n //= num
factor.append(num)
if n!=1:
factor.append(n)
return factor
n,m=list(map(int,input().split()))
mod=10**9+7
if m==1:
print((1))
quit()
li=trial_division(m)
tmp=li[0]
countli=[]
count=1
for i in range(1,len(li)):
if tmp!=li[i]:
countli.append(count)
count=1
else:
count+=1
tmp=li[i]
countli.append(count)
ans=1
for i in range(len(countli)):
ans*=combinations_count(countli[i]+n-1,countli[i])
print((ans%mod)) | import sys
import math
def input():
return sys.stdin.readline()[:-1]
def combinations_count(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
def trial_division(n):
factor = []
tmp = int(math.sqrt(n)) + 1
for num in range(2,tmp):
while n % num == 0:
n //= num
factor.append(num)
if n!=1:
factor.append(n)
return factor
n,m=list(map(int,input().split()))
mod=10**9+7
if m==1:
print((1))
quit()
li=trial_division(m)
tmp=li[0]
countli=[]
count=1
for i in range(1,len(li)):
if tmp!=li[i]:
countli.append(count)
count=1
else:
count+=1
tmp=li[i]
countli.append(count)
ans=1
for i in range(len(countli)):
r=countli[i]
s=n+r-1
r=min(r,n-1)
p=1
for j in range(r):
p*=s-j
p//=j+1
ans*=p
ans%=mod
print((ans%mod)) | p03253 |
from collections import Counter
def factorization(n) -> list:
if n==1:
return [1]
ret = []
i = 2
while i*i<=n:
while n%i==0:
n //= i
ret.append(i)
i += 1
if n!=1:
ret.append(n)
return ret
n,m = list(map(int,input().split()))
mod = 10**9+7
if m==1:
print((1));exit()
factors = Counter(factorization(m))
mx = n+max(factors.values())
fac = [1]*(mx+1)
inv = [1]*(mx+1)
for i in range(1,mx+1):
fac[i] = fac[i-1] * i % mod
inv[-1] = pow(fac[-1], mod - 2, mod)
for i in range(mx-1, -1, -1):
inv[i] = inv[i+1] * (i+1) % mod
def cmb(n,r):
assert n >= r >= 0
return fac[n] * inv[n-r] * inv[r] % mod
ans=1
for v in list(factors.values()):
ans*=cmb(n+v-1,v)
ans%=mod
print(ans) | from collections import Counter
def factorization(n) -> list:
if n==1:return [1]
ret = []
i = 2
while i*i<=n:
while n%i==0:
n //= i
ret.append(i)
i += 1
if n!=1:ret.append(n)
return ret
from operator import mul
from functools import reduce
def cmb(n,r):
if n < r:return 0
r = min(n-r,r)
if r==0:return 1
u = reduce(mul, list(range(n, n-r, -1)))
d = reduce(mul, list(range(1,r+1)))
return u//d
def main():
n,m = list(map(int,input().split()))
mod = 10**9+7
if m==1:
print((1))
exit()
ans=1
for v in list(Counter(factorization(m)).values()):
ans*=cmb(n+v-1,v)
ans%=mod
print(ans)
if __name__=="__main__":main() | p03253 |
#coding utf-8
import math
N,M=list(map(int,input().split()))
def soinsu(m):
fact =[]
i = 2
while i*i<=m:
if m%i==0:
fact.append(i)
m //=i
else:
i +=1
if m>1:
fact.append(m)
return fact
fact=soinsu(M)
counting=[]
for i in fact:
counting.append(fact.count(i))
del fact[:fact.count(i)-1]
if fact==[]:
break
def permi(n,r):
return math.factorial(n)//math.factorial(n-r)
def combi(n,r):
return permi(n,r)//math.factorial(r)
ans = 1
for i in counting:
ans *=combi(i+N-1,N-1)
print((ans%(10**9+7))) | #coding utf-8
import math
from operator import mul
from functools import reduce
N,M=list(map(int,input().split()))
def soinsu(m):
fact =[]
i = 2
while i*i<=m:
if m%i==0:
fact.append(i)
m //=i
else:
i +=1
if m>1:
fact.append(m)
return fact
fact=soinsu(M)
counting=[]
for i in fact:
counting.append(fact.count(i))
del fact[:fact.count(i)-1]
if fact==[]:
break
def combi(n,r):
r =min(r,n-r)
if r==0:
return 1
over = reduce(mul, list(range(n, n - r, -1)))
under = reduce(mul, list(range(1, r + 1)))
return over // under
ans = 1
for i in counting:
ans *=combi(i+N-1,N-1)
print((ans%(10**9+7))) | p03253 |
N, M = list(map(int, input().split()))
import math
def prime_fac(n):
p_lis = []
temp = n
for i in range(2, int(math.sqrt(n)) + 1):
if temp % i == 0:
cnt = 0
while temp % i == 0:
cnt += 1
temp //= i
p_lis.append([i, cnt])
if temp != 1:
p_lis.append([temp, 1])
if p_lis == []:
p_lis.append([n, 1])
return p_lis
mod = 10 ** 9 + 7
MAX = 10 ** 6
fac = [1, 1]
finv = [1, 1]
inv = [0, 1]
def comb(n, r):
if n < r:
return 0
else:
return fac[n] * ( finv[r] * finv[n-r] % mod ) % mod
for i in range(2, MAX + 1):
fac.append( ( fac[-1] * i ) % mod )
inv.append( mod - ( inv[mod % i] * (mod // i) % mod ) )
finv.append( finv[-1] * inv[-1] % mod )
ans = 1
for p, a in prime_fac(M):
if a == p == 1:
break
ans *= comb(N+a-1, a)
ans %= mod
print(ans) | N, M = list(map(int, input().split()))
import math
def prime_fac(n):
p_lis = []
temp = n
for i in range(2, int(math.sqrt(n)) + 1):
if temp % i == 0:
cnt = 0
while temp % i == 0:
cnt += 1
temp //= i
p_lis.append([i, cnt])
if temp != 1:
p_lis.append([temp, 1])
if p_lis == []:
p_lis.append([n, 1])
return p_lis
mod = 10 ** 9 + 7
MAX = N + 50
fac = [1, 1]
finv = [1, 1]
inv = [0, 1]
def comb(n, r):
if n < r:
return 0
else:
return fac[n] * ( finv[r] * finv[n-r] % mod ) % mod
for i in range(2, MAX + 1):
fac.append( ( fac[-1] * i ) % mod )
inv.append( mod - ( inv[mod % i] * (mod // i) % mod ) )
finv.append( finv[-1] * inv[-1] % mod )
ans = 1
for p, a in prime_fac(M):
if a == p == 1:
break
ans *= comb(N+a-1, a)
ans %= mod
print(ans) | p03253 |
import copy
N,M=list(map(int,input().split()))
mod=10**9+7
#x以下の素数の列挙
import math
x=math.floor(math.sqrt(10**9))
L=math.floor(math.sqrt(x))#平方根を求める
Primelist=[i for i in range(x+1)]
Primelist[1]=0#素数でないものは0にする.
for i in Primelist:
if i>L:
break
if i==0:
continue
for j in range(2*i,x+1,i):
Primelist[j]=0
Primes=[Primelist[j] for j in range(x+1) if Primelist[j]!=0]
def fact(M):#約数の列挙
if M==1:
return {1}
DICT=dict()#素因数分解
i=0
while M!=1 and i<len(Primes):
if M%Primes[i]==0:
DICT[Primes[i]]=DICT.get(Primes[i],0)+1
M=M//Primes[i]
else:
i+=1
if M!=1:
DICT[M]=1
VALUES=list(DICT.values())
KEYS=list(DICT.keys())
LIST=[1]
for i in range(len(DICT)):
NOWLIST=copy.copy(LIST)
for l in NOWLIST:
for j in range(0,VALUES[i]+1):
LIST.append(l*KEYS[i]**j)
return set(LIST)
def Combi2(a,b):#aは大きいが、bは小さいとき
if b>a:
return 0
ANS=1
for i in range(min(b,a-b)):
ANS=ANS*(a-i)%mod*pow(min(b,a-b)-i,mod-2,mod)%mod
return ANS%mod
SET=fact(M)
factor=dict()
for j in SET:
factor[j]=fact(j)
DP=dict()
defaultans=[0 for i in range(40)]
defaultans[1]=1
defaultans=tuple(defaultans)
def dp(m):
ANS=[0 for i in range(40)]
if m==1:
return defaultans
for j in factor[m]:
#print(j,factor[m])
if j==1:
continue
else:
if DP.get(m//j,-1)!=-1:
NEXT=DP[m//j]
else:
NEXT=dp(m//j)
for k in range(39):
ANS[k+1]=(ANS[k+1]+NEXT[k])%mod
#print(m//j,ANS,NEXT)
DP[m]=ANS
return ANS
LIST=dp(M)
ANS=0
for i in range(40):
if LIST[i]!=0:
ANS=ANS+Combi2(N,i-1)*LIST[i]%mod
print((ANS%mod))
| N,M=list(map(int,input().split()))
mod=10**9+7
import math
L=math.floor(math.sqrt(M))
X=dict()
for i in range(2,L+2):
while M%i==0:
X[i]=X.get(i,0)+1
M=M//i
if M!=1:
X[M]=X.get(M,0)+1
def Combi2(a,b):#aは大きいが、bは小さいとき
if b>a:
return 0
ANS=1
for i in range(min(b,a-b)):
ANS=ANS*(a-i)*pow(min(b,a-b)-i,mod-2,mod)
return ANS%mod
ANS=1
for x in list(X.values()):
ANS=(ANS*Combi2(x+N-1,x))%mod
print(ANS) | p03253 |
import math
import collections
def trial_division_sqrt(n):
prime_count = collections.Counter()
for i in range(2, int(math.sqrt(n)) + 2):
while n % i == 0:
n /= i
prime_count[i] += 1
if n > 1:
prime_count[n] += 1
return prime_count
def pc(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
s=0
x,N = list(map(int,input().split()))
li = trial_division_sqrt(N)
li = li.most_common()
ans = 1
for i in range(0, len(li)):
ans *= pc(li[i][1] + x-1, x-1)
print((ans % (pow(10, 9)+7))) | import math
import collections
def trial_division_sqrt(n):
prime_count = collections.Counter()
for i in range(2, int(math.sqrt(n)) + 2):
while n % i == 0:
n /= i
prime_count[i] += 1
if n > 1:
prime_count[n] += 1
return prime_count
def pc(n, r):
return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
nCr = {}
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;
s=0
x,N = list(map(int,input().split()))
li = trial_division_sqrt(N)
li = li.most_common()
ans = 1
for i in range(0, len(li)):
ans *= cmb(li[i][1] + x-1, x-1)
print((ans % (pow(10, 9)+7))) | p03253 |
import sys
input = sys.stdin.readline
from collections import *
def prime_fact(n):
prime = Counter()
m = 0
while not n % 2:
prime[2] += 1
n //= 2
m += 1
x = 3
while x**2 <= n:
c = 0
while not n % x:
prime[x] += 1
n //= x
c += 1
m = max(m, c)
x += 2
if n > 1: prime[n] += 1
return prime, m
MOD = 10**9+7
class Comb:
def __init__(self, N):
self.fac = [1] * (N+5)
for i in range(2, N+5): self.fac[i] = self.fac[i-1] * i % MOD
def pow(self, a, b):
res = 1
while b:
if b & 1: res = res * a % MOD
a = a**2 % MOD
b >>= 1
return res
def comb(self, n, r):
if r < 0 or r > n: return 0
return (self.fac[n] * self.pow(self.fac[r], MOD-2)) % MOD * self.pow(self.fac[n-r], MOD-2) % MOD
def main():
N, M = list(map(int, input().split()))
prime, m = prime_fact(M)
comb = Comb(N-1+m)
ans = 1
for v in list(prime.values()):
ans = ans * comb.comb(N-1+v, v) % MOD
print(ans)
if __name__ == '__main__':
main() | N, M = list(map(int, input().split()))
MOD = 10**9+7
class Comb:
def __init__(self, N):
self.fac = [1] * (N+1)
for i in range(2, N+1): self.fac[i] = self.fac[i-1] * i % MOD
def pow(self, a, b):
res = 1
while b:
if b & 1: res = res * a % MOD
a = a**2 % MOD
b >>= 1
return res
def comb(self, n, r):
if r < 0 or r > n: return 0
return (self.fac[n] * self.pow(self.fac[r], MOD-2)) % MOD * self.pow(self.fac[n-r], MOD-2) % MOD
def permutation(self, n, r):
if r == 0: return 1
return self.fac[n] * self.pow(self.fac[n-r], MOD-2) % MOD
from collections import *
import sys
def get_prime(n):
c = Counter()
while not n % 2:
c[2] += 1
n //= 2
i = 3
while i**2 <= n:
while not n % i:
c[i] += 1
n //= i
i += 2
if n > 1:
c[n] += 1
return c
prime = get_prime(M)
if not prime: print((1)); sys.exit()
comb = Comb(N+max([m for m in list(prime.values())]))
ans = 1
for n in list(prime.values()):
ans = ans * comb.comb(N+n-1, n) % MOD
print((ans % MOD)) | p03253 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.