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())
id = [-1] * M
lis = []
tot = 0
le = 0
while id[X] == -1:
    id[X] = le
    le += 1
    lis.append(X)
    tot += X
    X = (X**2) % M

c = le - id[X]
sm = 0
for i in range(id[X],le):
    sm += lis[i]
if (N <= le):
    ans = 0
    for i in range(N):
        ans += lis[i]
    print(ans)
    exit()

ans = tot
N -= le
ans += N // c * sm
N %= c
for i in range(id[X],id[X]+N):
    ans += lis[i]
print(ans)
