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
# -*- coding: utf-8 -*-
# 標準入力を取得
N, X, M = list(map(int, input().split()))

# 求解処理
s = {X}
l = [X]
i = 0
while True:
    a = l[-1]**2 % M
    if a in s:
        i = l.index(a)
        break
    else:
        s.add(a)
        l.append(a)

loop_length = len(l) - i
loop_cnt = (N - i) // loop_length
loop_res = (N - i) % loop_length
ans = sum(l[:i]) + loop_cnt * sum(l[i:]) + sum(l[i: i + loop_res])

# 結果出力
print(ans)
