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=list()
ans=0
s=n
for i in range(n):
    ans+=x
    a.append(x)
    x=(x**2)%m
    if x in a:
        s=a.index(x)
        break

sum=0
if s!=n:
    for i in range(s, len(a)):
        sum+=a[i]   

if len(a)>s:
    ans+=sum*(((n-s)//(len(a)-s))-1)

    z=(n-s)%(len(a)-s)
    if z!=0:
        for i in range(z):
            ans+=a[s+i]
print(ans)
