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())

ans = []
flag = False
for i in range(n):
    if x in ans:
        v = x
        flag = True
        break
    ans.append(x)
    x = x**2 % m
if flag:
    p = ans.index(v)
    l = len(ans) - p
    d, e = divmod(n-p, l)
    print(sum(ans[:p]) + d*sum(ans[p:]) + sum(ans[p:p+e]))
else:
    print(sum(ans))
