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
import sys

n,x,m = (int(i) for i in input().split())
l = [x]
ans = x
memo_array = [-1]*(m+1)

for i in range(1,n):
    ans = ans**2%m
    idx = memo_array[ans]
    if idx != -1:
        loop_num, mod = divmod((n-idx),(i-idx))
        print(sum(l[:idx]) + sum(l[idx:])*(loop_num)+sum(l[idx:idx+mod]))
        sys.exit()
    l.append(ans)
    memo_array[ans]=i
print(sum(l))