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())
i = X%M
L = [i]
S = set([i])
i = i**2 % M
while not i in S:
    L.append(i)
    S.add(i)
    i = i**2 % M
index = L.index(i)
k = (N-index)//len(L[index:])
l = (N-index)%len(L[index:])

# これでうまくいくのたまたまだよ。本当はN<indexの場合分けがひつよう。なんで場合分けするよ
if N<index:
    ans = sum(L[:N])
else:
    ans = sum(L[:index]) + (k*sum(L[index:])) + sum(L[index:index+l])
print(ans)