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=[0 for i in range(m)]
ans=0
y=[]
i=1
flag=0
ys=n
while i<n+1:
    if flag==0:
        ans+=x
    l[x]+=1
    x=x*x%m
    i+=1
    if l[x]==2 and flag==0:
        flag=1
        ys=i
    if flag:
        if l[x]==3:
            break
        y.append(x)
if len(y):
    p,pp=divmod(n-ys,len(y))
    print(ans+p*sum(y)+sum(y[:pp+1]))
    #print(ans,p*sum(y),sum(y[:pp+1]))
else:
    print(ans)