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())
c1 = [X]
c2 = {X}
ans = X
for i in range(N-1):
    X = pow(X,2,M)
#    print(X)
    if X not in c2:
        c1.append(X)
        c2.add(X)
        ans += X
    else:
        b = c1.index(X)
        break
else:
    print(ans)
    exit()
l = len(c1) - b
t = N-i -1
ans += (t//l) * sum(c1[b:]) + sum(c1[b:b+t%l])
print(ans)