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())
T = []
K = [0]*M
p = X
for i in range(N):
    if K[p] == 1:
        break
    else:
        T.append(p)
    K[p] = 1
    p *= p
    p %= M

for i in range(N):
    if T[i] == p:
        break
ans = 0
ans += sum(T)
if N > len(T):
    L = sum(T[i:])
    q = len(T[i:])
    ans += L*((N-len(T))//q)
    ans += sum(T[i:i+(N-len(T)) % q])
print(ans)