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())
def am(a, b):
    return (a * a) % b
l = [x]
u = []
now = x
for i in range(n):
    s = am(now, m)
    if(s in l):
        break
    l.append(s)
    now = s
c = l.index(s)
k = 0
if(0 in l):
    print(sum(l))
else:
    for i in range(c):
        u.append(l.pop(0))
    a = (n-len(u)) // len(l)
    b = (n-len(u)) % len(l)
    print(sum(u) + a * sum(l) + sum(l[:b]))
