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
M=10**9+7;D=[];i=1;r=0;N,K=map(int,input().split())
while i*i<=N:
	if N%i==0:D.append(i);i*i<N and D.append(N//i)
	i+=1
D.sort();N=[]
for i in range(len(D)):
	N.append(pow(K,-~D[i]//2,M))
	for j in range(i):
		if D[i]%D[j]==0:N[i]=(N[i]-N[j])%M
	r=(r+(N[i]*D[i]*pow(2,M-2+D[i]%2,M)))%M
print(r)