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())
A = []
al = [-1]*(m+1)
cnt = 0
for i in range(n):
    if al[x%m] >= 0:
        break
    al[x%m] = cnt
    A.append(x)
    cnt += 1   
    x = x**2 % m

if n <= al[x]:
    print(sum(A[:al[x]]))
    exit()

lena = len(A)
loop = A[al[x]:]
lenl = cnt-al[x]
n -= al[x]
cnt = n//lenl
print(sum(A[:al[x]]) + sum(loop)*cnt + sum(loop[:n%lenl]))