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
li = [a]
exists = dict()
i = 1
for i in range(2, n + 1):
    a = a * a % m
    if a in exists:
        break
    li.append(a)
    exists[a] = i

ans = sum(li)
if i != n:
    loop, left = divmod(n - i + 1, i - exists[a])
    ans += loop * sum(li[exists[a]-1:]) + sum(li[exists[a]-1:exists[a]-1+left])
print(ans)
