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())
result = [x]
for i in range(m):
    y = (result[-1] * result[-1]) % m
    if y in result:
        start = result.index(y)
        end = i
        break
    result.append(y)

loop = result[start:]
a = start
b = (n - a) // len(loop)
c = (n - a) % len(loop)
ans = sum(result[:a]) + (sum(loop) * b) + sum(loop[:c])
print(ans)