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