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())

s = set()
l = [x]
while x ** 2 % m not in s:
    v = x ** 2 % m
    s.add(v)
    l.append(v)
    x = v

idx = l.index(x ** 2 % m)
loop = len(l) - idx

if n < len(l):
    print(sum(l[:n]))
elif (n - idx) % loop == 0:
    print(sum(l[:idx]) + ((n - idx) // loop) * sum(l[idx:]))
else:
    print(sum(l[:idx]) + ((n - idx) // loop) * sum(l[idx:]) + sum(l[idx:idx+(n-idx)%loop]))