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())
D = [-1]*M
A = [X]
for i in range(M):
    if D[X]>=0: break
    D[X] = i
    X = X * X % M    
    A.append(X)

st = D[X]
loop = A[st:-1]

if N<=st:
    ans = sum(A[:N])
else:
    Nl = N-st
    ans = sum(A[:st]) + sum(loop)*(Nl//len(loop)) + sum(loop[:Nl%len(loop)])
print(ans)
