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())

f = [-1]*m
ans = x
n -= 1
while n > 0:
    if f[x] == -1:
        f[x] = pow(x, 2, m)
        ans += f[x]
        x = f[x]
        n -= 1
    else:
        break
loop = [x]
ans -= x
for i in range(n):
    tmp = pow(loop[-1], 2, m)
    if tmp == loop[0]:
        break
    loop.append(tmp)
loopsum = sum(loop)
ans += (n+1) // len(loop) * loopsum + sum(loop[0:((n+1) % len(loop))])
print(ans)
