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 = set()

for i in range(3 * 10 ** 6):
    nx = (A[-1]** 2) % M
    if nx in S:
        break
    S.add(nx)
    A.append(nx)

L = []
R = []
for i, a in enumerate(A):
    if a != nx:
        L.append(a)
    else:
        R = A[i:]
        break

ans = sum(L)
N -= len(L)

RS = sum(R)
ans += RS * (N // len(R))
if R:
    for i in range(N % len(R)):
        ans += R[i]

print(ans)
