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,mod=map(int,input().split())
d=[-1]*mod
ans=0
syu=0
al=[]
for i in range(n):
    if d[x]!=-1:
        en=i
        syu=i-d[x]    
        break
    ans+=x
    al.append(x)
    d[x]=i
    x=x*x%mod   
if syu==0:
    print(ans)
    exit()
ans+=((n-en)//syu)*sum(al[d[x]:en])
for i in range((n-en)%syu):
    ans+=x%mod
    x=x*x%mod
print(ans)