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 = [int(x) for x in input().split()]
A = [x]
while len(A) < n:
    a = (A[-1] * A[-1]) % m
    if a not in A:
        A.append(a)
    else:
        i = A.index(a)
        loop_len = len(A) - i
        print(sum(A[:i]) + sum(A[i:]) * ((n - i) // loop_len) + sum(A[i:i + ((n - i) % loop_len)]))
        break
else:
    print(sum(A))
