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
def resolve():
    n,x,m = map(int,input().split())
    ans = x
    y = [x]
    for i in range(n-1):
        x = (x**2)%m
        if x not in y:
            y.append(x)
        else:
            break
    b = y.index(x)
    N = len(y[b:])
    c = sum(y[b:])
    ans = sum(y[:b]) + c*((n-b)//N)+sum(y[b:b+(n-b)%N])
    print(ans)
resolve()