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())

mod=[0]*(m)

mod[x%m]=1
ans=x

for i in range(2,n+1):
    x=(x**2)%m
    #print(i,x)
    if mod[x]==0:
        ans+=x
        mod[x]=i
    else:
        #過去に2度来たことがある
        if mod[x]==-1:
            break
        #過去に1度来たことがある
        else:
            turn=i-mod[x]
            ans+=x*(((n-i)//turn+1))
            mod[x]=-1

print(ans)


    


