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
# coding: utf-8
# Your code here!
import sys
readline = sys.stdin.readline
read = sys.stdin.read

n,x,m = map(int, readline().split())
#lr = [list(map(int, readline().split())) for _ in range(k)]


nxt = [x*x%m for x in range(m)]
wa = list(range(m))
ans = 0

while n:
    if n&1:
        ans += wa[x]
        x = nxt[x]
    wa = [wa[nxt[i]] + wa[i] for i in range(m)]    
    nxt = [nxt[i] for i in nxt]
    n >>= 1

print(ans)