Takahashi and Aoki are going to together construct a sequence of integers.

First, Takahashi will provide a sequence of integers a, satisfying all of the following conditions:

* The length of a is N.
* Each element in a is an integer between 1 and K, inclusive.
* a is a palindrome, that is, reversing the order of elements in a will result in the same sequence as the original.



Then, Aoki will perform the following operation an arbitrary number of times:

* Move the first element in a to the end of a.



How many sequences a can be obtained after this procedure, modulo 10^9+7?

Constraints

* 1≤N≤10^9
* 1≤K≤10^9

Input

The input is given from Standard Input in the following format:


N K


Output

Print the number of the sequences a that can be obtained after the procedure, modulo 10^9+7.

Examples

Input

4 2


Output

6


Input

1 10


Output

10


Input

6 3


Output

75


Input

1000000000 1000000000


Output

875699961
#include <bits/stdc++.h>
using namespace std;

static const int mod = 1000000007;

inline void inc(int &x, int y) { (x += y) >= mod && (x -= mod); }
inline int mul(int x, int y) { return 1LL * x * y - 1LL * x * y / mod * mod; }
inline int modpower(int x, int y) {
  int res = 1;
  while (y) {
    if (y & 1) res = mul(res, x);
    y >>= 1, x = mul(x, x);
  }
  return res;
}

int n, k, ans;
int F[10000];
int main() {
  scanf("%d %d", &n, &k);
  vector<int> factor;
  for (int i = 1; i * i <= n; ++i) {
    if (n % i == 0) {
      factor.push_back(i);
      if (i * i != n) factor.push_back(n / i);
    }
  }
  sort(factor.begin(), factor.end());
  ans = 0;
  for (int i = 0; i < (int)factor.size(); ++i) {
    int x = factor[i];
    F[i] = modpower(k, (x + 1) / 2);
    for (int j = 0; j < i; ++j)
      if (x % factor[j] == 0) inc(F[i], mod - F[j]);
    inc(ans, mul(F[i], (x & 1) ? x : x / 2));
  }
  printf("%d\n", ans);
  return 0;
}