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]
S = [0, X]
Y = [-1] * M
f = 0
s = X
for i in range(1, M * 5 + 10):
    a = A[-1] ** 2 % M
    s += a
    A.append(a)
    S.append(s)
    if f == 0 and Y[a] >= 0:
        rp = i - Y[a]
        t = Y[a]
        f = 1
    Y[a] = i
if N < M * 5 * 0:
    print(S[N])
else:
    j = N % rp + (t // rp + 1) * rp
    print(S[j] + (S[t + rp] - S[t]) * (N - j) // rp)