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.
#include <bits/stdc++.h>
using namespace std;
long long int power(long long int t, long long int x) {
  long long int ans = 1;
  while (t > 0) {
    if (t % 2 == 1) ans = (ans * x) % 1000000007;
    t = t / 2;
    x = (x * x) % 1000000007;
  }
  return ans % 1000000007;
}
void prime(long long int n, vector<long long int>& v) {
  map<long long int, long long int> m;
  while (n % 2 == 0) {
    n = n / 2;
    if (m[2] == 0) {
      v.push_back(2);
      m[2] = 1;
    }
  }
  for (long long int i = 3; i * i <= n; i++) {
    while (n % i == 0) {
      if (m[i] == 0) {
        v.push_back(i);
        m[i] = 1;
      }
      n = n / i;
    }
  }
  if (n > 2) v.push_back(n);
}
int main() {
  std::ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long int x, n;
  cin >> x >> n;
  vector<long long int> v;
  prime(x, v);
  map<long long int, long long int> p;
  ;
  for (long int i = 0; i < v.size(); i++) {
    long long int m = n;
    while (m >= v[i]) {
      p[v[i]] += (m / v[i]);
      m = m / v[i];
    }
  }
  long long int ans = 1;
  ;
  for (long int i = 0; i < v.size(); i++) {
    ans = (ans * (power(p[v[i]], v[i]))) % 1000000007;
  }
  cout << ans % 1000000007;
  return 0;
}
