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())

s = 0
mt = []
def f(x):
    return x**2 % M
i = 0
while True:
    i += 1
    mt.append(X)
    a = f(X)
    if i == N:
        f = 1
        break
    elif a in mt:
        f = 0
        break
    else:
        X = a

if f == 1:
    print(sum(mt))
else:
    e = mt.index(a)
    s1 = mt[:e]
    s2 = mt[e:]
    l = i - e
    c, d = divmod(N - e, l)
    print(sum(s1) + sum(s2) * c + sum(s2[:d]))