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
import sys
input = lambda: sys.stdin.readline().rstrip("\r\n")

n, x, m = map(int, input().split())
s = set([x])
l = [x]
for i in range(m):
    x = x**2 % m
    if x in s:
        start_index = l.index(x)
        break
    else:
        s.add(x)
        l.append(x)
ans = sum(l[:start_index])

q = l[start_index:]
p = (n - start_index) // len(q)
ans += sum(q) * p
ans += sum(q[:(n - p*len(q) - start_index)])
print(ans) 