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;

const int mod=1000000007;
typedef long long ll;
int ksm(ll a,int b,int c=1){
	for(;b;b/=2,a=a*a%mod)
		if(b&1)c=c*a%mod;
	return c;
}

inline void reduce(int&x){x+=x>>31&mod;}
int n,K,ans;
vector<pair<int,int> >factor(int n){
	vector<pair<int,int> >ret;
	for(int i=1;i*i<=n;++i)if(n%i==0)ret.emplace_back(i,0),ret.emplace_back(n/i,0);
	sort(ret.begin(),ret.end());
	return ret;
}

int main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin>>n>>K;
	auto vec=factor(n);
	for(auto&i:vec){
		int res=ksm(K,(i.first+1)/2);
		for(auto j:vec)if(i.first%j.first==0)reduce(res-=j.second);
		i.second=res;res=(ll)res*i.first/(2-(i.first&1))%mod;
		reduce(ans+=res-mod);
	}
	cout<<ans<<'\n';
	return 0;
}
