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
rp=[x]
if n<=m:
    for i in range(n-1):
        x=pow(x,2,m)
        ans+=x
    print(ans)
    exit()
for i in range(m+1):
    x=pow(x,2,m)
    if x in rp:
        tt=rp.index(x)
        t=len(rp)-tt
        break
    else:
        rp.append(x)
tmp=sum(rp[tt:])
wari=(n-tt)//t
amari=(n-tt)%t
ans=sum(rp[:tt])+tmp*wari+sum(rp[tt:tt+amari])
print(ans)