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())
i=int(2)
a=[x]
q=int(0)
while (i <= n) and (q == 0):
	x=(x**2)%m
	if x in a:
		q=1
	else:
		a.append(x)
	i=i+1

if len(a) == n:
	print(sum(a))	
else:
	j=a.index(x)
	b=a[0:j]
	c=a[j:]
	lb=len(b)
	lc=len(c)
	k=(n-lb)%lc
	l=(n-lb)//lc
	d=c[0:k]
	print(sum(b)+sum(c)*l+sum(d))