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())
visited = [(-1,-1)]*M
ans = 0
for i in range(N):
    if visited[X][0] >= 0:
        d = ans - visited[X][0]
        left = N-i
        length = i-visited[X][1]
        ans += (left//length)*d
        left %= length
        for j in range(left):
            ans += X
            X = X*X % M
        break
    visited[X] = (ans, i)
    ans += X
    X = X*X % M
print(ans)