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 = list(map(int,input().split()))

D = [X]

E = set([X])

F = [0,X]

for i in range(M+1):
    X = X**2
    X%=M
    if X in E:
        break
    D.append(X)
    E.add(X)
    F.append(F[-1]+X)
if N<=len(D):
    print(F[N])
else:
    for i in range(len(D)):
        if D[i]==X:
            break
    #print(D)
    num = (N-i-1)//(len(D)-i)
    res = (N-i-1)%(len(D)-i)
    print(F[res+i+1] + num*(F[-1]-F[i]))