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())

def cal(x):
    return pow(x,2,M)

memo = set()
lis = []
while X not in memo:
    memo.add(X)
    lis.append(X)
    X = cal(X)
pos = lis.index(X)

if pos >= N:
    print(sum(lis[:N]))
else:
    print(sum(lis[:pos]) + ((N-pos)//(len(memo)-pos)) * sum(lis[pos:]) + sum(lis[pos:(N-pos)%(len(memo)-pos)+pos]))