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())
A = [X]
As = set(A)
Lstart = 0
for i in range(N):
    An = A[-1]**2 % M
    if An in As:
        Lstart = A.index(An)
        break
    else:
        A.append(An)
        As.add(An)
LenBefL = Lstart
LenLoop = len(A) - Lstart
if LenLoop > 0:
    ans = sum(A[:Lstart])+sum(A[Lstart:])*((N-LenBefL)//LenLoop) + sum(A[Lstart:Lstart + (N-LenBefL)%LenLoop])
else:
    ans = sum(A)
print(ans)