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<stdio.h>
#include<math.h>
#include<algorithm>
using namespace std;
long long mod=1000000007;
long long pw(long long a,long long b){
	long long ret=1;
	while(b){
		if(b%2)ret=ret*a%mod;
		a=a*a%mod;
		b/=2;
	}
	return ret;
}
int y[2100];
long long ks[2100];

int main(){
	int a,b;scanf("%d%d",&a,&b);
	long long ret=0;
	int sz=0;
	for(int i=1;i*i<=a;i++){
		if(a%i==0){
			y[sz++]=i;
			if(i*i!=a)y[sz++]=a/i;
		}
	}
	std::sort(y,y+sz);
	for(int i=0;i<sz;i++){
		long long cnt=pw(b,(y[i]+1)/2);
		for(int j=0;j<i;j++)if(y[i]%y[j]==0)cnt=(cnt+mod-ks[j])%mod;
		ks[i]=cnt;
		//printf("%d: %lld\n",y[i],cnt);
		if(y[i]%2)ret=(ret+cnt*y[i])%mod;
		else ret=(ret+cnt*y[i]/2)%mod;
	}
	printf("%lld\n",ret);
}

