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
import sys
input = sys.stdin.readline

N,X,M=map(int,input().split())
LIST=[X]
SET={X}

a=X

while True:
    if a*a%M in SET:
        break
    else:
        a=a*a%M
        LIST.append(a)
        SET.add(a)

l=LIST.index(a*a%M)
LEN=len(LIST)

if N<=LEN:
    print(sum(LIST[:N]))
else:
    ANS=sum(LIST[:l])
    N-=l
    LIST=LIST[l:]
    S=sum(LIST)

    r,q=divmod(N,len(LIST))

    print(ANS+S*r+sum(LIST[:q]))
    

