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())

flag = [False]*m
a = []
while not flag[x]:
    flag[x] = True
    a.append(x)
    x = pow(x, 2, m)
loop_start_idx = a.index(x)
loop_len = len(a) - loop_start_idx
loop_count = (n - loop_start_idx)//loop_len
loop_amari = (n-loop_start_idx)%loop_len
ans = sum(a[:loop_start_idx])
ans += sum(a[loop_start_idx:])*loop_count
ans += sum(a[loop_start_idx: loop_start_idx + loop_amari])
print(ans)
