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())
A=[X]
x=(A[0]**2)%M
i=0
while not x in A:
    A.append(x)
    i+=1
    x=(x**2)%M

loopid=A.index(x)
looplen=i-loopid+1
loopsum=sum(A[loopid:])
startsum=sum(A[:loopid])

ans=0
if N-1<loopid:
    ans=sum(A[:N])
else:
    loopnum=(N-1-loopid+1)//looplen if looplen else N-1-loopid
    rest=N-1-(loopid+looplen*loopnum)+1
    ans+=startsum
    ans+=loopnum*loopsum
    ans+=sum(A[loopid:loopid+rest])
print(ans)
