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())

dic = {}
a = x
s = 0
c = m
for i in range(1, n + 1):
    if a not in dic:
        s += a
        dic[a] = [i]
    elif len(dic[a]) == 1:
        s += a * (1 + (n - i) // (i - dic[a][0]))
        dic[a].append(i)
    else:
        break
    a = pow(a, 2, m)
print(s)