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.*;
import java.text.*;

public class Main {

    Scanner sc = new Scanner(System.in);

    int n = sc.nextInt();
    int m = sc.nextInt();

    List<Integer>[] lists = new ArrayList[n+1];

    //        2 ... n
    int[] res = new int[n+1];


    public static void main(String[] args) {
        new Main().run();
    }

    void run() {

        for (int i=0; i<n+1; i++) lists[i] = new ArrayList<>();

        for (int i=0; i<m; i++) {
            int s = sc.nextInt();
            int t = sc.nextInt();
            lists[s].add(t);
            lists[t].add(s);
        }

//        System.out.println(lists[1]);

        bfs(1);

        int cnt = 0;

        for (int i=2; i<=n; i++) {
            if (res[i] != 0) cnt++;
        }

        if (cnt != n-1) {
            System.out.println("No");
        } else {
            System.out.println("Yes");
            for (int i=2; i<=n; i++) {
                System.out.println(res[i]);
            }
        }



    }

    void bfs(int s) {
        Queue<Integer> queue = new ArrayDeque<>();
        queue.add(s);
        while (!queue.isEmpty()) {
            int t = queue.peek();
            for (int u: lists[t]) {
                if (res[u] == 0) {
                    res[u] = t;
                    queue.add(u);
                }
            }
            queue.poll();
        }
    }
}