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())
dp = [x]
s = set([x])
for i in range(1000000):
    if ((dp[-1] ** 2) % m) in s:
        dp.append((dp[-1] ** 2) % m)
        break
    s.add((dp[-1] ** 2) % m)
    dp.append((dp[-1] ** 2) % m)
ind = dp.index(dp[-1])
del dp[-1]
print(sum(dp[:ind]) + sum(dp[ind:]) * ((n - ind) // (len(dp) - ind)) + sum(dp[ind:ind + ((n - ind) % (len(dp) - ind))]))