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())
s=x
t={x}
u=[x]
for i in range(1,n):
    x=pow(x,2,m)
    if x==0:break
    if x==1:
        s+=n-i
        break
    if x in t:
        j=u.index(x)
        s=sum(u[:j])
        u=u[j:]
        s+=(n-j)//len(u)*sum(u)
        s+=sum(u[:(n-j)%len(u)])
        break
    s+=x
    t|={x}
    u+=x,
print(s)