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
b = x
box = [x]
c= 0
for i in range(1,n):
    b= (b**2)%m
    if b == 0:
        print(ans)
        exit() 
    if b in box:
        c = box.index(b)
        break
    ans += b
    box.append(b)
# print(c)
# print(sum(box)*(n//len(box)) + sum(box[0:n%len(box)]))


print(sum(box[:c])+sum(box[c:])*((n-c)//len(box[c:])) + sum(box[c:c+(n-c)%len(box[c:])]))
