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.ArrayDeque;
import java.util.ArrayList;
import java.util.Deque;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class Main {

    static class Pos {
        public int x;
        public int prev;

        public Pos(int x, int prev) {
            this.x = x;
            this.prev = prev;
        }
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        int[] a = new int[m];
        int[] b = new int[m];
        int[] ans = new int[n + 1];
        Map<Integer, List<Integer>> map = new HashMap<>();
        for (int i = 1; i <= n; i++) {
            map.put(i, new ArrayList<>());
        }
        for (int i = 0; i < m; i++) {
            a[i] = sc.nextInt();
            b[i] = sc.nextInt();
            List<Integer> alist = map.get(a[i]);
            alist.add(b[i]);
            map.put(a[i], alist);
            List<Integer> blist = map.get(b[i]);
            blist.add(a[i]);
            map.put(b[i], blist);
        }

        List<Integer> oneList = map.get(1);
        Deque<Pos> queue = new ArrayDeque<>();
        for (int i = 0; i < oneList.size(); i++) {
            queue.add(new Pos(oneList.get(i), 1));
        }
        while (!queue.isEmpty()) {
            int size = queue.size();
            for (int i = 0; i < size; i++) {
                Pos pos = queue.poll();
                int num = pos.x;
                int prev = pos.prev;

                if (ans[num] != 0) {
                    continue;
                }
                ans[num] = prev;
                List<Integer> l = map.get(num);
                for (int j = 0; j < l.size(); j++) {
                    queue.add(new Pos(l.get(j), num));
                }
            }
        }

        for (int i = 2; i <= n; i++) {
            if (ans[i] == 0) {
                System.out.println("No");
                return;
            }
        }
        System.out.println("Yes");
        for (int i = 2; i <= n; i++) {
            System.out.println(ans[i]);
        }
    }

}