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>
typedef long long i64;
const int P=1e9+7;
struct factor{
	int x,t,v;
	bool operator<(const factor&w)const{return x<w.x;}
}fs[3007];
int n,k,fp=0,ans=0;
void chk(int x){
	if(n&1)fs[fp++]=(factor){x,x+1>>1};
	else if(1&~(n/x))fs[fp++]=(factor){x,x};
}
int pw(int a,int n){
	int v=1;
	for(;n;n>>=1,a=i64(a)*a%P)if(n&1)v=i64(v)*a%P;
	return v;
}
int main(){
	scanf("%d%d",&n,&k);
	for(int i=1;i*i<=n;++i)if(n%i==0){
		chk(i);
		if(i*i!=n)chk(n/i);
	}
	std::sort(fs,fs+fp);
	for(int i=0;i<fp;++i){
		fs[i].v=pw(k,fs[i].t);
		for(int j=0;j<i;++j)if(fs[i].x%fs[j].x==0){
			(fs[i].v-=fs[j].v)%=P;
		}
		ans=(ans+fs[i].v*i64(fs[i].x))%P;
	}
	printf("%d\n",(ans+P)%P);
	return 0;
}