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())
table = [0]*(M+1)

pre = X
table[pre] = 0
seq = [pre]
cnt = 0
while True:
    cnt += 1
    A = pre**2%M
    if not table[A]:
        seq.append(A)
        table[A] = cnt
        pre = A
    else:
        f = table[A]
        s = cnt
        break
    
ans = 0
for i in range(f + (N-f)%(s-f)):
    ans += seq[i]
m = (N-f)//(s-f)
for i in range(f, s):
    ans += seq[i]*m

print(ans)