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())
ans=x
a=x
res=[x]
res2=0
r=0
for i in range(1,m+1):
    a=(a*a)%m
    if a==0:
        break
    if a in res:
        r=res.index(a)
        res2=i-r
        break
    else:
        ans+=a
        res.append(a)
b=[0]*m
for i in range(res2):
    b[i+1]=b[i]+res[r+i]
if res2==0:
    print(ans)
else:
    k=(n-r)//res2;l=(n-r)%res2
    ans+=b[res2]*(k-1)+b[l]
    print(ans)
