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<cstdio>
#include<algorithm>
#define int long long
#define mod 1000000007
int n,k,ans,dp[1001000],p[1001000],cnt;
int quickpow(int x,int y){
	if(y==0)return 1;
	if(y==1)return x;
	if(y%2==0)return quickpow(x*x%mod,y/2);
	if(y%2==1)return quickpow(x*x%mod,y/2)*x%mod;
}
signed main(){
	scanf("%lld%lld",&n,&k);
	for(int i=1;i*i<=n;i++)
		if(n%i==0){
			p[++cnt]=i;;
			if(i*i!=n)p[++cnt]=n/i;
		}
	std::sort(p+1,p+cnt+1);
	for(int i=1;i<=cnt;i++){
		dp[i]=quickpow(k,(p[i]+1)/2);
		for(int j=1;j<i;j++)
			if(p[i]%p[j]==0)dp[i]=(dp[i]-dp[j]+mod)%mod;
		if(p[i]%2==0)(ans+=dp[i]*p[i]/2%mod)%=mod;
		else(ans+=dp[i]*p[i]%mod)%=mod;
	}
	printf("%lld\n",ans);
}