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>

#define mod (1000000007)
#define rv2 (500000004)

int N, K;
std::map<int, int> d;
std::set<int> set;

int powmod(int a, int b){
	int ret = 1;
	while(b){
		if(b & 1) ret = (1ll) * ret * a % mod;
		b >>= 1;
		a = (1ll) * a * a % mod;
	}
	return ret;
}

int get_d(int i){
	int ret = powmod(K, (i + 1) / 2);
	for(int j = 1; j * j <= i; ++ j){
		if(i % j || j == i) continue;
		ret = (ret - d[j] + mod) % mod;
		if(i / j == j || i / j == i) continue;
		ret = (ret - d[i / j] + mod) % mod;
	}
	return ret;
}

int main(){
	scanf("%d%d", &N, &K);
	int ans = 0;
	for(int i = 1; i * i <= N; ++ i){
		if(N % i) continue;
		set.insert(i);
		set.insert(N / i);
	}
	for(auto i : set){
		d[i] = get_d(i);
		if(i % 2) ans = (ans + (1ll) * d[i] * i % mod) % mod;
		else ans = (ans + (1ll) * d[i] * i % mod * rv2 % mod) % mod;
	}
	printf("%d\n", ans);
	return 0;
}