Problem: There is a cave.

The cave has N rooms and M passages. The rooms are numbered 1 to N, and the passages are numbered 1 to M. Passage i connects Room A_i and Room B_i bidirectionally. One can travel between any two rooms by traversing passages. Room 1 is a special room with an entrance from the outside.

It is dark in the cave, so we have decided to place a signpost in each room except Room 1. The signpost in each room will point to one of the rooms directly connected to that room with a passage.

Since it is dangerous in the cave, our objective is to satisfy the condition below for each room except Room 1.

* If you start in that room and repeatedly move to the room indicated by the signpost in the room you are in, you will reach Room 1 after traversing the minimum number of passages possible.



Determine whether there is a way to place signposts satisfying our objective, and print one such way if it exists.

Constraints

* All values in input are integers.
* 2 \leq N \leq 10^5
* 1 \leq M \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq N\ (1 \leq i \leq M)
* A_i \neq B_i\ (1 \leq i \leq M)
* One can travel between any two rooms by traversing passages.

Input

Input is given from Standard Input in the following format:


N M
A_1 B_1
:
A_M B_M


Output

If there is no way to place signposts satisfying the objective, print `No`.

Otherwise, print N lines. The first line should contain `Yes`, and the i-th line (2 \leq i \leq N) should contain the integer representing the room indicated by the signpost in Room i.

Examples

Input

4 4
1 2
2 3
3 4
4 2


Output

Yes
1
2
2


Input

6 9
3 4
6 1
2 4
5 3
4 6
1 5
6 2
4 5
5 6


Output

Yes
6
5
5
1
1

Solution (in JAVA):

Solution:
import java.util.*;

public class Main {
    static int max = 1000000;
    static int[] queue = new int[max];
    static int tail = 0; static int head = 0;
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        init();
        int n = sc.nextInt();
        int m = sc.nextInt();
        HashMap<Integer,TreeSet<Integer>> graph = new HashMap<>();
        for (int i=1;i<=n;i++)graph.put(i,new TreeSet<Integer>());
        for (int i=0;i<m;i++){
            int a = sc.nextInt();
            int b = sc.nextInt();
            graph.get(a).add(b);
            graph.get(b).add(a);
        }
        //int[] depth = new int[n+1];
        //depth[1] = 0;
        boolean[] seen = new boolean[n+1];
        for (int i=0;i<=n;i++)seen[i]=false;
        enqueue(1);
        //int count = 1;
        int[] flag = new int[n+1];
        while (!isEmpty()){
            int v = dequeue();
            for (int a : graph.get(v)){
                if (!seen[a]){
                    seen[a]=true;
                    //depth[a]=count;
                    flag[a]=v;
                    enqueue(a);
                }
            }
            //count++;
        }
        System.out.println("Yes");
        for (int i=2;i<=n;i++)System.out.println(flag[i]);
    }

    static void init(){head = 0; tail = 0;}
    static boolean isEmpty(){return (head==tail);}
    static boolean isFull(){return (head == (tail+1)%max);}
    static public void enqueue(int v){
        if (isFull()){
            System.out.println("error: queue is full.");
            return;
        }
        queue[tail++] = v;
        if (tail == max) tail = 0;
    }
    static public int dequeue(){
        if (isEmpty()){
            System.out.println("error: queue is empty");
            return -1;
        }
        int res = queue[head];
        ++head;
        if (head == max) head = 0;
        return res;
    }
}