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())
arr = [x]
mod = x
memo = [-1 for _ in range(m+1)]

ans = 0
for i in range(1, n):
    mod = mod ** 2 % m
    idx = memo[mod]

    if idx != -1:
        a = i - idx
        q, _mod = divmod((n - idx), a)

        ans = sum(arr[0:idx]) + q * sum(arr[idx:idx+a]) + sum(arr[idx:idx+_mod])
        break
    arr.append(mod)
    memo[mod] = i

if ans == 0:
    ans = sum(arr)

print(ans)