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())

y=x
A=[]
A.append(y)
cnt=1
su=x

for i in range(m):
    y=(y**2)%m
    cnt+=1
    if y in A:
        break
    else:
        A.append(y)
        su+=y

c=A.index(y) #周期のはじめ
d=cnt-(c+1)  #周期のはじめから次の周期のはじめで個数を求める

e=sum(A[:c]) 
#周期に入るまえまでを足しておく


f=sum(A[c:c+(n-c)%d])
    #周期からはみでた最後の部分

g=su-e#1周期分
h=g*((n-c)//d)#かけざん

print(e+h+f)