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())
array = [0,X]
array2 = [X]
a = X
sum = X
valid = True
while(True):
    a = pow(a,2,M)
    if a in array2:
        y = array2.index(a)
        break
    sum += a
    array.append(sum)
    array2.append(a)
l = len(array2)
h = l - y
if N <= y:
    print(array[N])
else:
    ans = array[y] + (array[-1]-array[y])*((N-y)//h) + array[y+(N-y)%h] - array[y]
    print(ans)
