Let us denote by f(x, m) the remainder of the Euclidean division of x by m.

Let A be the sequence that is defined by the initial value A_1=X and the recurrence relation A_{n+1} = f(A_n^2, M). Find \displaystyle{\sum_{i=1}^N A_i}.

Constraints

* 1 \leq N \leq 10^{10}
* 0 \leq X < M \leq 10^5
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N X M


Output

Print \displaystyle{\sum_{i=1}^N A_i}.

Examples

Input

6 2 1001


Output

1369


Input

1000 2 16


Output

6


Input

10000000000 10 99959


Output

492443256176507
n,x,m=map(int,input().split())
p=[x]
A=set([x])
f=0
for i in range(n-1):
	p.append(p[-1]**2%m)
	if p[-1] in A:
		f=1
		break
	else:
		A.add(p[-1])
if f==0:
	print(sum(p))
else:
	for i in range(len(p)):
		if p[i]==p[-1]:
			loop=len(p)-i-1
			break
	SUM=sum(p[i:-1])
	ans=sum(p)-p[-1]
	n-=len(p)-1
	ans+=SUM*(n//loop)+sum(p[i:i+n%loop])
	print(ans)