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())
d={}
x=X
A=[]
init=0
loop=0
S=[0]
while x not in d:
    d[x]=1
    A.append(x)
    S.append(S[-1]+A[-1])
    x=x*x%M

init=A.index(x)
loop=len(A)-init

if N<=init+loop:
    print(S[N])
else:
    l=(N-init)//loop
    r=(N-init)%loop
    print((S[-1]-S[init])*l+S[init+r])

