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
#!/usr/bin python3
# -*- coding: utf-8 -*-

n, x, m = map(int, input().split())

s = set([])
v = []
for i in range(m+1):
    s.add(x)
    v.append(x)
    x = pow(x,2,m)
    if x in s:
        break
st = v.index(x)
lp = len(v)-st
lps = sum(v[st:])

k = (n-(st+lp)+(lp-1))//lp
ret = lps * k
n -= lp * k
ret += sum(v[:n])

print(ret)