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())
ans = 0
l = [x]
s = [0]*m
s[0] = 1

for i in range(n):
	x = (x*x)%m
	if s[x] == 1:
		break
	s[x] = 1
	l.append(x)

if x == 0:
	print(sum(l))
else:
	p = l[0]
	k = 1
	Su = 0
	while p != x and k < len(l):
		Su += p
		p = l[k]
		k += 1
	l = l[k-1:]

	Su2 = 0
	for r in range((n-k)%len(l) + 1):
		Su2 += l[r]
	print(Su + ((n-k)//len(l))*sum(l) + Su2)