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())

chk = [0 for i in range(m)]
a = x
s = x
c = 0
ary = [x]
flg = False
while True:
  if c == n:
    break
  x = (x**2)%m
  s += x
  c += 1
  if chk[x]:
    flg = True
    break
  ary.append(x)
  chk[x] = c
if flg == False:
  print (sum(ary[:-1]))
  exit()
cyc = ary[chk[x]:]
l1 = len(cyc)
ss = ary[:chk[x]]
l2 = len(ss)
tot = sum(ss) + sum(cyc)*((n-l2)//l1) + sum(cyc[:((n-l2)%l1)])
print (tot)