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 = (int(x) for x in input().split())
A = [x]
used = {x, }
while True:
    x = pow(x, 2, m)
    if x in used:
        index = A.index(x)
        break
    else:
        A.append(x)
        used.add(x)
if n <= len(A):
    print(sum(A[:n]))
else:
    ans = sum(A)
    n -= len(A)
    m = len(A) - index
    ans += (n // m) * sum(A[index:])
    ans += sum(A[index:index + (n % m)])
    print(ans)