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 = [x]
for _ in range(m):
    ans.append(pow(ans[-1], 2, m))
loop = [ans[-1]]
check = ans[-1]
for _ in range(m):
    next = pow(loop[-1], 2, m)
    if next == check:
        break
    else:
        loop.append(next)
if n <= m+1:
    A = sum(ans[:n])
else:
    times = (n - m) // len(loop)
    amari = (n - m) % len(loop)
    A = sum(ans[:-1]) + sum(loop) * times + sum(loop[:amari])
print(A)