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 std::sort;

const int N=1e5+10,Mod=1e9+7;

int n,k,que[N],dp[N];

void Init() {
	scanf("%d%d",&n,&k);
}

int pow(int x,int t) {
	int ret=1;
	while (t) {
		if (t&1) ret=1ll*ret*x%Mod;
		x=1ll*x*x%Mod;
		t=t>>1;
	}
	return ret;
}

void Solve() {
	int top=0;
	for (int i=1;i*i<=n;++i) {
		if (n%i) continue;
		que[++top]=i;
		if (i*i==n) continue;
		que[++top]=n/i;
	}
	sort(que+1,que+top+1);
	
	int ans=0;
	for (int i=1;i<=top;++i) {
		dp[i]=pow(k,(que[i]+1)>>1);
		for (int j=1;j<i;++j) if (que[i]%que[j]==0) {
			dp[i]=(dp[i]-dp[j]+Mod)%Mod;
		}
		if (que[i]&1) ans=(ans+1ll*dp[i]*que[i]%Mod)%Mod;
		else ans=(ans+1ll*dp[i]*que[i]/2%Mod)%Mod;
	}
	
	printf("%d\n",ans);
}

int main() {
	Init();
	Solve();
	return 0;
}