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())
id=[-1 for i in range(m+1)]
s=[]
c=0
while id[x]==-1:
    id[x]=c
    c+=1
    s.append(x)
    x=x*x%m
d=c-id[x]
ans=0
if n<=d:
    for i in range(n):
        ans+=s[i]
else:
    for i in range(id[x]):
        ans+=s[i]
    n-=id[x]
    sum=0
    for i in range(d):
        sum+=s[id[x]+i]
    ans+=(n//d)*sum
    n=n%d
    for i in range(n):
        ans+=s[id[x]+i]
print(ans)