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())
a=[]
mod_check_list = [False for _ in range(m)]
a.append(x*x%m)
ind=0
s=0
for i in range(m):
    t=a[i]*a[i]%m
    if mod_check_list[t]:
        ind=a.index(t)
        break
    mod_check_list[t] = True
    a.append(t)
s=sum(a[ind:])
l=len(a)-ind
loop_times = (n-1-ind)//l
answer=loop_times*s
for i in range((n-1-ind)%l):
    answer+=a[i+ind]
print(answer+x+sum(a[:ind]))