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 = [int(_) for _ in input().split()]
seen = {}
i = 0
A = []
while True:
    if X in seen:
        i2 = seen[X]
        i3 = i
        break
    seen[X] = i
    A += [X]
    i += 1
    X = X**2 % M
if N < i3:
    ans = sum(A[:N])
elif i2 == i3:
    ans = sum(A[:i2]) + A[i2] * (N - i2)
else:
    q, r = divmod(N - i2, i3 - i2)
    ans = sum(A[:i2]) + sum(A[i2:]) * q + sum(A[i2:i2 + r])
print(ans)
