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 = list(map(int, input().split()))
i = 1
a = X
s = 0
L = []
while i < N and a > 0:
    L.append(a)
    s += a
    a = (a**2) % M
    if a in L:
        j = L.index(a)
        break
    i += 1
else:
    s += a
    print(s)
    exit()

# print(L)
t = sum(L[:j])
L = L[j:]
u = s-t
N = N-j
v = t+u*(N//(i-j))
if N % (i-j) == 0:
    pass
else:
    v += sum(L[:N % (i-j)])
print(v)
