Problem:
Score: 400 points

Problem Statement

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.

Sample Input 1

4 4
1 2
2 3
3 4
4 2

Sample Output 1

Yes
1
2
2

If we place the signposts as described in the sample output, the following happens:

Starting in Room 2, you will reach Room 1 after traversing one passage: (2) \to 1. This is the minimum number of passages possible.

Starting in Room 3, you will reach Room 1 after traversing two passages: (3) \to 2 \to 1. This is the minimum number of passages possible.

Starting in Room 4, you will reach Room 1 after traversing two passages: (4) \to 2 \to 1. This is the minimum number of passages possible.

Thus, the objective is satisfied.

Sample Input 2

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

Sample Output 2

Yes
6
5
5
1
1

If there are multiple solutions, any of them will be accepted.

Solution in C (GCC 9.2.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <stdbool.h>

int main()
{
  int n, m;
  scanf("%d %d", &n, &m);
  int Distance[n][n];
  for (int i = 0; i < n; i++)
  {
    for (int j = 0; j < n; j++)
    {
      Distance[i][j] = -1;
    }
  }
  int a, b;
  for (int i = 0; i < m; i++)
  {
    scanf("%d %d", &a, &b);
    Distance[a - 1][b - 1] = 1;
    Distance[b - 1][a - 1] = 1;
  }
  for (int i = 0; i < n; i++)
  {
    Distance[i][i] = 0;
  }

  int nPoint = n;

  int sp = 0, dp = 1;
  printf("Yes\n");
  while (dp < n)
  {

    int sRoute[nPoint]; /* 出発地から目的地までの最短経路上の地点の地点番号を目的地から出発地の順に設定する1次元配列 */
    int sDist;          /* 出発地から目的地までの最短距離 */

    /* その他使う変数 */
    int pDist[nPoint]; /* 出発地から各地点までの最短距離を設定する配列 */
    int pRoute[nPoint];
    bool pFixed[nPoint]; /* 出発地から各地点までの最短距離が確定しているかどうかを識別するための配列 */
    int sPoint, i, j, newDist;

    sDist = 999999; /* 出発地から目的地までの最短距離に初期値を格納する（変更しなくてよい） */

    for (i = 0; i < nPoint; i++)
    {
      sRoute[i] = -1;    /* 最短経路上の地点の地点番号に初期値を格納する */
      pDist[i] = 999999; /* 出発地から各地点までの最短距離に初期値を格納する */
      pFixed[i] = false; /* 各地点の最短距離の確定状態に初期値を格納する */
    }

    pDist[sp] = 0; /* 出発地から出発地自体への最短距離に0を設定する */

    while (true)
    { /* 最短経路探索処理 */
      i = 0;
      while (i < nPoint)
      { /* 未確定の地点を1つ探す */
        if (pFixed[i] == 0)
        {
          break; /* 再内側の繰り返しから抜ける */
        }
        i = i + 1;
      }

      if (i == nPoint)
      {        /* 出発地から全ての地点までの最短経路が確定していれば */
        break; /* 最短経路探索処理を抜ける */
      }

      for (j = i + 1; j < nPoint; j++)
      { /* 最短距離がより短い地点を探す */
        if ((pFixed[j] == 0) && (pDist[j] < pDist[i]))
        {
          i = j;
        }
      }

      sPoint = i;
      pFixed[sPoint] = true; /* 出発地からの最短距離を確定する */

      for (j = 0; j < nPoint; j++)
      {
        if ((Distance[sPoint][j] > 0) && (pFixed[j] == 0))
        {
          newDist = pDist[sPoint] + Distance[sPoint][j];
          if (newDist < pDist[j])
          {
            pDist[j] = newDist;
            pRoute[j] = sPoint;
          }
        }
      }
    }

    sDist = pDist[dp];
    j = 0;
    i = dp;
    while (i != sp)
    {
      sRoute[j] = i;
      i = pRoute[i];
      j = j + 1;
    }
    sRoute[j] = sp;

    printf("%d\n", sRoute[1] + 1);
    dp++;
  }

  return 0;
}