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
import sys
readline = sys.stdin.readline

N,X,M = map(int,readline().split())
nex = [0] * M # 次に進む先を持つリスト ダブリング時は「次の次」になる
sums = [0] * M # その点での総和を持つリスト　ダブリング時は「現時点の総和と次の総和の和」になる

for i in range(M):
  nex[i] = i * i % M
  sums[i] = i

ans = 0
while N:
  if N & 1:
    ans += sums[X]
    X = nex[X]
  sums = [sums[i] + sums[nex[i]] for i in range(M)]
  nex = [nex[nex[i]] for i in range(M)]
  N >>= 1
  
print(ans)