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())

isUsed = [False] * M
isUsed[X] = True
S = [X]
st = X
while True:
    nx = X**2 % M
    if isUsed[nx]:
        st = nx
        break
    isUsed[nx] = True
    S.append(nx)
    X = nx

idx = S.index(st)
L, R = S[:idx], S[idx:]

ans = sum(L[:N])
N = max(0, N - len(L))

q, r = divmod(N, len(R))
ans += q * sum(R) + sum(R[:r])

print(ans)