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())

lst, num = set(), []
for i in range(n):
    lst.add(x), num.append(x)
    x = x ** 2 % m
    if x in lst:
        cnt, idx = i + 1, num.index(x)
        break

ans = sum(num)
if x in lst:
    div, mod = divmod(n - cnt, len(num) - idx)
    ans += sum(num[idx:]) * div
    ans += sum(num[idx:idx + mod])
print(ans)
