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())
Flag = [True]*(M)

A = []
temp = X

while Flag[temp]:
  A.append(temp)
  Flag[temp] = False
  temp = (temp**2)%M
  last = temp

I = A.index(last)
looplen = len(A) - I
loop, cnt = divmod(max(N-I, 0), looplen)

ans = 0
if N <= I+1:
  ans += sum(A[:N])
else:
  ans += sum(A[:I])
  ans += loop*sum(A[I:])
  ans += sum(A[I:I+cnt])

print(ans)