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())
set_a = set()
a = []
while len(a)<n:
    if x in a:break
    set_a.add(x)
    a.append(x)
    x = x**2%m

ans = sum(a[:min(n,len(a))])
n -= len(a)
if n<1:
    print(ans)
    exit()

i = a.index(x)
l = len(a)-i
ans += sum(a[i:]) * (n//l)
n %= l
ans += sum(a[i:i+n])
print(ans)

