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())

order = []
hist = [0] * M

for i in range(N):
    if hist[X]:
        j = order.index(X)
        rem = N-i
        d,m = divmod(rem,i-j)
        for k in order[j:]:
            hist[k] += d
        for k in order[j:j+m]:
            hist[k] += 1
        break
    order.append(X)
    hist[X] += 1
    X = (X*X)%M

ans = 0
for i,h in enumerate(hist):
    ans += i*h
print(ans)