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>
#define ysf (1000000007)
int a[3005],f[3005],n,k,tot,ans;
inline int qpow(int a,int b){
  int ans=1;
  while (b){
    if (b&1) ans=1LL*ans*a%ysf;
    if (b>>=1) a=1LL*a*a%ysf;
  }
  return ans;
}
int main(){
  std::cin>>n>>k;
  for (int i=1;i*i<=n;++i){
    if (n%i) continue; a[++tot]=i;
    if (i*i!=n) a[++tot]=n/i;
  }
  std::sort(a+1,a+tot+1);
  for (int i=1;i<=tot;++i){
    f[i]=qpow(k,(a[i]+1)>>1);
    for (int j=1;j<i;++j)
      if (!(a[i]%a[j])) f[i]-=f[j],f[i]<0?f[i]+=ysf:0;
    if (a[i]&1) ans=(ans+1LL*a[i]*f[i])%ysf;
    else ans=(ans+1LL*a[i]*f[i]/2)%ysf;
  }
  std::cout<<ans; return 0;
}
