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([x])
t = [x]
p = 1
for i in range(n):
    x = x * x % m
    if x in s:
        break
    else:
        s.add(x)
        t.append(x)
    p += 1
if p == n:
    print(sum(s))
    exit()

q = t.index(x)
l = p - q
b = sum(t[q:p])
ans = sum(t[:q])
n -= q
ans += n // l * b + sum(t[q:q + n % l])
print(ans)
