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]
p=[-1]*(M+1)
p[X]=0
x=0
for i in range(N-1):
    x=(l[-1]**2)%M
    if p[x]>=0:
        break
    l.append(x)
    p[x]=i+1
x=p[x]
y=len(l)-x
print(sum(l[:x])+(N-x)//y*sum(l[x:])+sum(l[x:x+(N-x)%y]))