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())
num = {x}
num2 = [x]
while True:
    temp = num2[-1] ** 2 % m
    if temp in num:
        break
    else:
        num.add(temp)
        num2.append(temp)
temp2 = num2.index(temp)
num3 = num2[:temp2]
num4 = num2[temp2:]
ans = sum(num3) + sum(num4) * ((n - len(num3)) // len(num4)) + sum(num4[:(n - len(num3)) % len(num4)])
print(ans)