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())

acc = [0]
S = dict()
Ai = X
i = 0
while Ai not in S:
    S[Ai] = i
    acc.append(acc[-1] + Ai)
    i += 1
    Ai = (Ai * Ai) % M

t = S[Ai]
T = i - t
if N <= t:
    ans = acc[N]
else:
    ans = acc[t] + (acc[-1] - acc[t]) * ((N - t) // T) 
    if (N - t) % T > 0:
        ans += acc[((N - t) % T) + t] - acc[t]
print(ans)
