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())

l = [X]
a = X
k = 0
for i in range(M):
    if a**2%M not in l:
        l.append(a**2%M)
        a = a**2%M
    else:
        k = l.index(a**2%M)
        break
sum = 0
for i in range(k,len(l)):
    sum += l[i]

ans = 0

ans += ((N-k)//(len(l)-k))*sum

for i in range(min(k,N)):
    ans += l[i]

for i in range(1,(N-k)%(len(l)-k)+1):
    ans += l[k+i-1]

print(ans)
