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.*;

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

class Solver {

    public void run() {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();

        int[] A = new int[M];
        int[] B = new int[M];

        List<List<Integer>> to = new ArrayList<>(100005);
        for (int i = 0; i < 100005; i++) {
            to.add(new ArrayList<Integer>());
        }

        for (int i = 0; i < M; i++) {
            A[i] = sc.nextInt();
            B[i] = sc.nextInt();

            A[i]--;
            B[i]--;

            to.get(A[i]).add(B[i]);
            to.get(B[i]).add(A[i]);
        }

        int[] dist = new int[100005];
        Arrays.fill(dist, -1);
        int[] pare = new int[100005];
        Arrays.fill(pare, -1);

        dist[0] = 0;
        Queue<Integer> queue = new LinkedList<Integer>();
        queue.offer(0);
        while (!queue.isEmpty()) {
            int v = queue.poll();

            for (Integer nv : to.get(v)) {
                if (dist[nv] < 0) {
                    dist[nv] = dist[v] + 1;
                    pare[nv] = v;
                    queue.offer(nv);
                }
            }
        }

        for (int i = 0; i < N; i++) {
            if (i == 0) continue;
            if (dist[i] < 0) {
                System.out.println("No");
                return;
            }
        }

        System.out.println("Yes");
        for (int i = 0; i < N; i++) {
            if (i == 0) continue;
            int p = pare[i];
            p++;
            System.out.println(p);
        }

        return;
    }

}