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]
where = {x: 0}
a = x
for i in range(1, n):
    a = A[-1]**2 % m
    if a in where:
        break
    where[a] = i
    A.append(a)

perstart = where[a]
res = sum(A)
rem = n - len(A)
per = len(A) - perstart
res += rem//per*sum(A[perstart:perstart+per])
res += sum(A[perstart:perstart + (rem%per)])

print(res)
