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]
found = {x}
while True:
    y = (a[-1] ** 2) % m
    a.append(y)
    if y in found:
        break
    found.add(y)
if n <= len(a):
    print(sum(a[:n]))
else:
    z = a.index(a[-1])
    a.pop()
    n -= z
    res = sum(a[:z])
    res += sum(a[z:]) * (n // (len(a) - z))
    res += sum(a[z:z + (n % (len(a) - z))])
    print(res)
