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] * (m + 1)
F = [None] * m
F[x] = 0
i0, j0 = None, None
for i in range(1, m + 1):
    S[i] = S[i - 1] + a
    a = pow(a, 2, m)
    if F[a] is not None:
        i0, j0 = F[a], i
    F[a] = i
q, r = (n - i0) // (j0 - i0), (n - i0) % (j0 - i0)
print((S[j0] - S[i0]) * q + S[i0 + r])
