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())
A = [0, x]
d = {x:1}
for i in range(2, n+1):
    A.append(A[i-1]**2 % m)
    if A[i] in d:
        j = d[A[i]]
        q, r = divmod(n-j+1, i-j)
        print(sum(A[:j]) + q*sum(A[j:i]) + sum(A[j:j+r]))
        break
    else:
        d[A[i]] = i
else:
    print(sum(A))