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())

a = x
r = [True for _ in range(m)]
s = []
while(r[a]):
  r[a] = False
  s.append(a)
  a = pow(a,2,m)
ai = s.index(a)
c = (n-len(s))//(len(s)-ai)
d = (n-len(s))-(len(s)-ai)*c
# print(i,ai,c,d)
ans = sum(s)+sum(s[ai:])*c+sum(s[ai:ai+d])
print(ans)