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())
g = x * 1
ans = x
arr = []
res = set([])
loop = (0, 0)
k = 0
for i in range(m + 1):
	tmp = x ** 2 % m
	if tmp in res:
		loop = (i, tmp)
		break
	res.add(tmp)
	arr.append(tmp)
	ans += tmp
	x = tmp

for i, y in enumerate(arr):
	if y == loop[1]:
		k = i
		break

ini = g + sum(arr[:k])
mul = ans - ini
t, v = divmod(n - k - 1, loop[0] - k)
print(ini + mul * t + sum(arr[k:k + v]))
