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 = X
ALL_cal = [False] * M
ALL = []
rou = False
for i in range(N-1):
    X = pow(X, 2, M)
    if ALL_cal[X]:
        num = ALL_cal[X]
        now = i
        rou = True
        break
    ALL.append(X)
    ALL_cal[X] = i
    ans += X
if rou :
    roupe = now - num 
    nokori = N - now - 1
    print(sum(ALL[num:])*(nokori//roupe) + ans + sum(ALL[num:num + nokori%roupe]))
else:
    print(ans)