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())
cur = X
pos = {}
path = []
i = 0
while cur not in pos:
    pos[cur] = i
    path.append(cur)
    cur = cur ** 2 % M
    i += 1

loop_start = pos[cur]
ans = None
if N <= len(path):
    ans = sum(path[:N])
else:
    ans = sum(path)
    left = N - len(path)
    q, r = divmod(left, len(path) - loop_start)
    ans += q * sum(path[loop_start:]) + sum(path[loop_start:loop_start + r])
print(ans)