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())

id = [-1] * M
a = []
l = 0
tot = 0
while id[X] == -1:
    a.append(X)
    id[X] = l
    l += 1
    tot += X
    X = X ** 2 % M

c = l - id[X]
s = 0
for i in range(id[X], l):
    s += a[i]

ans = 0
if N <= l:
    for i in range(N):
        ans += a[i]
else:
    ans += tot
    N -= l
    ans += s * (N // c)
    N %= c
    for i in range(N):
        ans += a[id[X] + i]

print(ans)
