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;


typedef long long int64;
const int mod = 1e9 + 7;

inline int64 modPow(int64 x, int64 n)
{
  if(n == 0) return (1);
  int64 ret = modPow(x, n / 2);
  (ret *= ret) %= mod;
  if(n & 1) (ret *= x) %= mod;
  return (ret);
}

int main()
{
  int N, K;
  cin >> N >> K;
  vector< int > divisor;
  for(int i = 1; i * i <= N; i++) {
    if(N % i == 0) {
      divisor.push_back(i);
      if(i * i != N) divisor.push_back(N / i);
    }
  }
  sort(begin(divisor), end(divisor));
  vector< int64 > dp(divisor.size());
  int64 ret = 0LL;
  for(int i = 0; i < divisor.size(); i++) {
    dp[i] = modPow(K, (divisor[i] + 1) / 2);
    for(int j = 0; j < i; j++) {
      if(divisor[i] % divisor[j] == 0) (dp[i] += mod - dp[j]) %= mod;
    }
    if(divisor[i] % 2 == 0) ret += divisor[i] / 2 * dp[i] % mod;
    else ret += divisor[i] * dp[i] % mod;
    ret %= mod;
  }
  cout << ret << endl;
}