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())

p=[0]*(M+2)
sum=[0]*(M+2)
p[X]=1
sum[1]=X
f=0
for i in range(2,N+1):
    X=(X**2)%M  
    if p[X]!=0:
        j=p[X]
        f=i
        break
    else:
        sum[i]=X+sum[i-1]
        p[X]+=i

if f==0:
    print(sum[N])
else:
    d,mod=divmod(N-j+1,i-j)
    print(d*(sum[i-1]-sum[j-1])+sum[j+mod-1])