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())
li = [x]
se = {x}
for i in range(n-1):
    x = x*x%m
    if x in se:
        idx = li.index(x)
        break
    li.append(x)
    se.add(x)
else:
    print(sum(li))
    exit(0)
ans = sum(li) + sum(li[idx:])*((n-len(li)) // (len(li)-idx)) + sum(li[idx:idx+(n-len(li)) % (len(li)-idx)])
print(ans)