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())

d = {}
l = []
for i in range(N):
    if X in d:
        break
    d[X] = i
    l.append(X)
    X = X*X%M
else:
    print(sum(l))
    exit()

s = d[X]

q, r = divmod(N-s,i-s)
ans = sum(l[:s])+q*sum(l[s:i])+sum(l[s:s+r])
print(ans)