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())
tt = [i*i % m for i in range(m)]
ss = [i for i in range(m)]


def merge(to1, s1, to2, s2):
    to3 = [to2[to1[i]] for i in range(m)]
    s3 = [s1[i] + s2[to1[i]] for i in range(m)]
    return to3, s3


t = [i for i in range(m)]
s = [0] * m
while n:
    if n % 2 == 1:
        t, s = merge(t, s, tt, ss)
    tt, ss = merge(tt, ss, tt, ss)
    n //= 2

print(s[x])
