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())
k_1 = set()
k_2 = set()
tmp = list()
loop_number = 0
loop_sum = 0
while x not in k_1:
	k_1.add(x)
	x = x*x%m
while x not in k_2:
	k_2.add(x)
	tmp.append(x)
	loop_number+=1
	loop_sum+=x 
	x = x*x%m
ans = 0
k_1 = list(k_1)
for i in range(len(k_1)):
	ans +=  k_1[i]
ans = ans + loop_sum * ((n-len(k_1))//loop_number)
for i in range((n-len(k_1))%loop_number):
	ans += tmp[i]
print(ans)