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())

arr = [x]
s = set()
s.add(x)
h = -1
r = 0
for i in range(n - 1):
	val = arr[-1]**2 % m
	if val not in s:
		arr += [arr[-1]**2 % m]
		s.add(arr[-1])
	else:
		h = i
		r = val
		break


res = sum(arr)
if h != -1:
	new_arr = arr[arr.index(r):]
	rest = n - (h + 1)
	c = len(new_arr)
	q = rest // c
	ssum = sum(new_arr) * q
	r = rest % c
	for i in range(r):
		ssum += new_arr[i]
	res += ssum	
	
print(res)