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 CPP):

Solution:
#include <cstdio>
#include <queue>
#include <vector>
typedef std::vector<int> vin;
const int MAXN = 2e5+5;
vin  G[MAXN];
int up[MAXN]{ };
int M, N;
int A, B;

void bfs(int src) {
  std::queue<int> Q;
  up[src] = src;
  Q.push(src);
  while (!Q.empty()) {
    int u = Q.front();
    Q.pop();
    for (int v: G[u]) {
      if (up[v]) continue;
      up[v] = u;
      Q.push(v);
    }
  }
}

int main() {
  scanf(" %d%d", &N, &M);
  for (int i = 0; i < M; ++i) {
    scanf(" %d%d", &A, &B);
    G[A].push_back(B);
    G[B].push_back(A);
  }
  bfs(1);
  puts("Yes");
  for (int i = 2; i <= N; ++i) {
    printf("%d\n", up[i]);
  }
  return 0;
}