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 = [int(_) for _ in input().split()]

def f(x, m):
    return x % m

P = [-1 for _ in range(M+1)]

A = [X]
for i in range(N-1):
    v = f(A[-1] ** 2, M)
    A.append(v)
    if P[v] != -1:
        break
    P[v] = i

v = f(A[-1] ** 2, M)
idx = P[v]

S = sum(A[idx+1:])
q, r = divmod(N - len(A), len(A) - idx - 1)

ans = sum(A) + q * S + sum(A[idx+1:idx+1+r])
print(ans)
