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
C = [0]
Xd = [-1] * (M+1)

for i in range(N):
    x = X if i==0 else x**2 % M
    
    if Xd[x] > -1:
        break
    Xd[x] = i
    ans += x
    C.append(ans)

loop_len = i - Xd[x]
if loop_len > 0:
    S = C[i] - C[Xd[x]]
    loop_num = (N - i) // loop_len
    ans += loop_num * S
    m = N - loop_num * loop_len - i
    ans += C[Xd[x]+m] - C[Xd[x]]

print(ans)