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())

tmp = [x]
while x**2%m not in tmp:
    x = x**2%m
    tmp.append(x)

cnt = len(tmp)
x = x**2%m

if n <= cnt:
    print(sum(tmp[:n]))
    exit()

for i in range(len(tmp)):
    if tmp[i] == x:
        st = sum(tmp[:i])
        rp = tmp[i:]
        div, mod = divmod(n-i, len(rp))
        en = sum(rp[:mod])
        print(st+sum(rp)*div+en)
        exit()