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
from collections import defaultdict
N,X,M=map(int,input().split())
cnt=0
index=[X]
d=defaultdict(int)
i=1
while True:
	X=pow(X,2,M)
	if d[X]!=0:
		z=d[X]
		break
	d[X]=i
	i+=1
	index.append(X)
target=len(index)-z
total=0
for i in range(z,len(index)):
	total+=index[i]
for i in range(z):
	cnt+=index[i]
total2=0
for i in range(z,z+(N-z)%target):
	total2+=index[i]
cnt+=total*((N-z)//target)+total2
print(cnt)