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())

amari = [x]
amariset = {x}
cnt = 0
p = 0

for i in range(n-1):
	a = amari[-1]**2 % m
	if a in amariset:
		p = amari.index(a)
		cnt = i+1-p
		break
	else:
		amari.append(a)
		amariset.add(a)

if cnt == 0:
	print(sum(amari))
	
else:
	n -= len(amari)
	a = n // cnt
	b = n % cnt
	print(sum(amari)+a*sum(amari[p:])+sum(amari[p:(p+b)]))