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 ll;
const int MAXN=1e5+10,MOD=1e9+7;
int n,k,dvs[MAXN],dp[MAXN],tot,res=0;

ll quick_pow(ll a,ll b)
{
	ll ret=1;
	for(;b;b>>=1,a=a*a%MOD)
		if(b&1) ret=ret*a%MOD;
	return ret;
}

int main()
{
	scanf("%d%d",&n,&k);
	for(int i=1;i*i<=n;i++)
		if(n%i==0)
		{
			dvs[++tot]=i;
			if(i*i!=n) dvs[++tot]=n/i;
		}
	sort(dvs+1,dvs+tot+1);
	for(int i=1;i<=tot;i++)
	{
		dp[i]=quick_pow(k,(dvs[i]+1)/2);
		for(int j=1;j<=i-1;j++)
			if(dvs[i]%dvs[j]==0) dp[i]=(dp[i]-dp[j]+MOD)%MOD;
		if(dvs[i]%2==0) (res+=1ll*dp[i]*dvs[i]/2%MOD)%=MOD;
		else (res+=1ll*dp[i]*dvs[i]%MOD)%=MOD;
	}
	printf("%d",res);
	return 0;
}