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())
l=[x]
c=1
d=-1
f=0
while(x>0 and c<n):
    g=(x*x)%m
    d=g
    if(g in l):
        f=1
        break
    l.append(g)
    x=g
    c+=1
s=sum(l)
if(f==1):
    r=l.index(g)
    o=(n-c)//(c-r)
    t=(n-c)%(c-r)
    s+=o*(sum(l[r:]))+sum(l[r:r+t])
print(s)
