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())

S = {X : 1}

path = [X]

cnt = 1
ans = X
a = X
for i in range(2, N + 1):
    a = a * a % M
    if a in S:
        cnt = i - S[a]
        break
    S[a] = i

    ans += a
    path.append(a)

pre_len = S[a] - 1

Q, R = divmod(N - pre_len - 1, len(path) - pre_len)

pre = sum(path[:pre_len])
cycle = sum(path) - pre

ans = a
for _ in range(R):
    a = a * a % M
    ans += a

print(pre + Q * cycle + ans)
