Let's introduce some definitions that will be needed later.

Let prime(x) be the set of prime divisors of x. For example, prime(140) = \{ 2, 5, 7 \}, prime(169) = \{ 13 \}.

Let g(x, p) be the maximum possible integer p^k where k is an integer such that x is divisible by p^k. For example:

  * g(45, 3) = 9 (45 is divisible by 3^2=9 but not divisible by 3^3=27), 
  * g(63, 7) = 7 (63 is divisible by 7^1=7 but not divisible by 7^2=49). 



Let f(x, y) be the product of g(y, p) for all p in prime(x). For example:

  * f(30, 70) = g(70, 2) ⋅ g(70, 3) ⋅ g(70, 5) = 2^1 ⋅ 3^0 ⋅ 5^1 = 10, 
  * f(525, 63) = g(63, 3) ⋅ g(63, 5) ⋅ g(63, 7) = 3^2 ⋅ 5^0 ⋅ 7^1 = 63. 



You have integers x and n. Calculate f(x, 1) ⋅ f(x, 2) ⋅ … ⋅ f(x, n) mod{(10^{9} + 7)}.

Input

The only line contains integers x and n (2 ≤ x ≤ 10^{9}, 1 ≤ n ≤ 10^{18}) — the numbers used in formula.

Output

Print the answer.

Examples

Input


10 2


Output


2


Input


20190929 1605


Output


363165664


Input


947 987654321987654321


Output


593574252

Note

In the first example, f(10, 1) = g(1, 2) ⋅ g(1, 5) = 1, f(10, 2) = g(2, 2) ⋅ g(2, 5) = 2.

In the second example, actual value of formula is approximately 1.597 ⋅ 10^{171}. Make sure you print the answer modulo (10^{9} + 7).

In the third example, be careful about overflow issue.
import sys
from collections import defaultdict
from itertools import combinations
from itertools import permutations
input = lambda : sys.stdin.readline().rstrip()
def write(*args, sep="\n"):
  for i in args:
    sys.stdout.write("{}".format(i) + sep)
INF = float('inf')
MOD = int(1e9 + 7)

def prime(x):
  ret = []
  for i in range(1, int(x**0.5) + 1):
    if x % i == 0:
      ret.append(i)
      if i * i != x:
        ret.append(x // i)
  
  ret2 = []
  
  for i in ret:
    flag = True 
    for j in range(2, int(i**0.5) + 1):
      if i % j == 0:
        flag = False
        break 
    if flag:
      ret2.append(i)
  
  ret2.remove(1)
  return ret2 # list(set(ret2))

#print(prime(169))

x, n = map(int, input().split())
ans = 1
p = prime(x)

# print(p)


for i in p:
  s = 0
  for j in reversed(range(1, 65)):
    temp = i ** j
    if temp > n:
      continue
    else:
      #print(n, temp, n // temp, s)
      ans *= pow(temp, n//temp - s, MOD)
      ans %= MOD 
      s += n // temp  - s
      ans %= MOD
      

print(ans % MOD) 