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())

tmp = []

while True:
    tmp.append(x)
    x = pow(x, 2, m)
    if x in tmp:
        break

k = 0
while True:
    if tmp[k] == x:
        break
    k += 1

if k > n:
    print(sum(tmp[:n]))
else:
    t = k
    a = (n - k) // (len(tmp) - k)
    s = (n - k) % (len(tmp) - k)
    print(sum(tmp[:k]) + sum(tmp[k:]) * a + sum(tmp[k: k + s]))



