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())
hist = [-1] * (M + 1)
ans = X; hist[X] = 0; A = [X]
r = X % M
i = 1
N -= 1
while N:
    nxt = (r * r) % M
    if hist[nxt] != -1:
        break
    ans += nxt
    hist[nxt] = i; A.append(nxt); i += 1
    r = nxt; N -= 1
if N:
    A_sub = A[hist[nxt]:]
    L = len(A_sub)
    q, rem = divmod(N, L)
    ans += sum(A_sub) * q + sum(A_sub[:rem])
print(ans)