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())

existence = [0] * M
a = []
A = X
for i in range(N):
    if existence[A] != 0:
        break
    existence[A] = 1
    a.append(A)
    A = A * A % M

for i in range(len(a)):
    if a[i] == A:
        break
j = i

result = sum(a[:j])
a = a[j:]
N -= j
x = N // len(a)
y = N % len(a)
result += sum(a) * x + sum(a[:y])
print(result)