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())

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

a = x
a_set = {a}
a_array = [a]
a_index = 0
while(True):
    a = f(a ** 2, m)
    if a in a_set:
        a_index = a_array.index(a)
        break
    a_set.add(a)
    a_array.append(a)


a_iter_array = a_array[a_index:]
div, mod = divmod(n - a_index, len(a_iter_array))
ans = sum(a_array[:a_index]) + sum(a_iter_array) * div + sum(a_iter_array[:mod])
print(ans)