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
S = [0, a]
lasts = [None] * (10 ** 5)
for i in range(1, N):
    a = (a * a) % M
    if a == 0:
        break
    if lasts[a] is not None:
        LA = lasts[a]
        T = i - LA
        print(S[-1] + (S[-1]-S[-T-1])*((N-i)//T) + S[-T-1+(N-i)%T] - S[-T-1])
        exit()
    S.append(S[-1] + a)
    lasts[a] = i

print(S[-1])
