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())

ans = 0
flag = [0]*(10**5 + 2)
lst = [X]

for i in range(N):
    X = (X**2)%M

    if flag[X] == 1:
        break

    flag[X] = 1
    lst.append(X)

preindex = lst.index(X)

preloop = lst[:preindex]
loop = lst[preindex:]

loopnum = (N - len(preloop))//len(loop)
loopafternum = (N - len(preloop))%len(loop)

ans = sum(preloop) + sum(loop)*loopnum + sum(loop[:loopafternum])
print(ans)