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())

idx = [-1] * M
A = []
total = 0
length = 0

while idx[X] == -1:
    A.append(X)
    idx[X] = length
    length += 1
    total += X
    X = pow(X, 2, M)

cycle = length - idx[X]
cycle_sum = sum(A[idx[X]:length])

ans = 0
if length >= N:
    print(sum(A[:N]))
else:
    ans += total
    N -= length
    l, m = divmod(N, cycle)
    ans += cycle_sum * l
    ans += sum(A[idx[X]:idx[X] + m])
    print(ans)
