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=map(int, sys.stdin.readline().split())

A=[]
A.append(X)
visit={}
for i in range(M+1):
    X=pow(X,2,M)
    if X not in visit:
        visit[X]=1
        A.append(X)
    else:
        break
loop_point=A.index(X)
notloop=A[:loop_point]
loop=A[loop_point:]

len_notloop=len(notloop)
len_loop=len(loop)


SUM_notloop=[0]
for x in notloop:
    SUM_notloop.append(SUM_notloop[-1]+x)


SUM_loop=[0]
for x in loop:
    SUM_loop.append(SUM_loop[-1]+x)

ans=0
if len_notloop<N:
    ans+=SUM_notloop[-1]
    N-=len_notloop
    sho,amari=N/len_loop,N%len_loop
    ans+=SUM_loop[-1]*sho
    ans+=SUM_loop[amari]
elif N<=len_notloop:
    ans=SUM_notloop[N]
print ans
