Problem Description

Give a number n, find the minimum x(x>0) that satisfies 2^x mod n = 1.

Input

One positive integer on each line, the value of n.

Output

If the minimum x exists, print a line with 2^x mod n = 1.

Print 2^? mod n = 1 otherwise.

You should replace x and n with specific numbers.

Sample Input

2

5

Sample Output

2^? mod 2 = 1

2^4 mod 5 = 1

题意很简单，就不用说了吧。

这个题主要就是会超范围，在这里，可以用取余的方法解决整数范围问题。

然后暴力就可以了。

首先防范一下n为偶数和等于1的情况。

import java.util.Scanner;

public class Main{

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);

        while(sc.hasNext()){

            int n  = sc.nextInt();

            if(n%2==0||n==1){

                System.out.println("2^? mod "+n+" = 1");

                continue;

            }

            int x=1;

            boolean is = true;

            for(int i=1;i<5000;i++){

                x=x*2;

                x=x%n;

                if(x%n==1){

                    is=false;

                    System.out.println("2^"+i+" mod "+n+" = 1");

                    break;

                }

            }

            if(is){

                System.out.println("2^? mod "+n+" = 1");

            }

        }

    }

}