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())

i = 0
a = x
aa = set()
aal = []
s = 0
while a not in aa:
    aa.add(a)
    aal.append(a)
    s += a
    i += 1
    if i == n:
        print(s)
        exit(0)
    a = (a ** 2) % m
    if a == 0:
        print(s)
        exit(0)
st  = aal.index(a)
cont = aal[st:]
nc = len(cont)
n -= st
ans = sum(aal[:st]) + sum(cont) * (n // nc) + sum(cont[:(n % nc)])
print(ans)