Problem:
Score : 500 points

Problem Statement

There is a rooted tree (see Notes) with N vertices numbered 1 to N.
Each of the vertices, except the root, has a directed edge coming from its parent.
Note that the root may not be Vertex 1.

Takahashi has added M new directed edges to this graph.
Each of these M edges, u \rightarrow v, extends from some vertex u to its descendant v.

You are given the directed graph with N vertices and N-1+M edges after Takahashi added edges.
More specifically, you are given N-1+M pairs of integers, (A_1, B_1), ..., (A_{N-1+M}, B_{N-1+M}), which represent that the i-th edge extends from Vertex A_i to Vertex B_i.

Restore the original rooted tree.

Notes

For "tree" and other related terms in graph theory, see the article in Wikipedia, for example.

Constraints

3 \leq N

1 \leq M

N + M \leq 10^5

1 \leq A_i, B_i \leq N

A_i \neq B_i

If i \neq j, (A_i, B_i) \neq (A_j, B_j).

The graph in input can be obtained by adding M edges satisfying the condition in the problem statement to a rooted tree with N vertices.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_{N-1+M} B_{N-1+M}

Output

Print N lines.
In the i-th line, print 0 if Vertex i is the root of the original tree, and otherwise print the integer representing the parent of Vertex i in the original tree.

Note that it can be shown that the original tree is uniquely determined.

Sample Input 1

3 1
1 2
1 3
2 3

Sample Output 1

0
1
2

The graph in this input is shown below:

It can be seen that this graph is obtained by adding the edge 1 \rightarrow 3 to the rooted tree 1 \rightarrow 2 \rightarrow 3.

Sample Input 2

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

Sample Output 2

6
4
2
0
6
2

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <string.h>

int e[110000][2];
int f[110000];
int q[110000], q1, q2;
int root[110000];
int fc[110000];

int main()
{
  int n, m;
  scanf("%d%d", &n, &m);
  int r = 1;
  memset(f, 0, sizeof(f));
  memset(fc, 0, sizeof(f));
  for (int i = 1; i <= n + m - 1; ++i)
  {
    int a, b;
    scanf("%d%d", &a, &b);
    e[i][0] = b;
    e[i][1] = f[a];
    f[a] = i;
    if (b == r) r = a;
    ++fc[b];
  }
  memset(root, 0, sizeof(root));
  q[0] = r;
  q1 = 0;
  q2 = 1;
  while (q1 < q2)
  {
    int x = q[q1++];
    for (int i = f[x]; i != 0; i = e[i][1])
    {
      if (--fc[e[i][0]] == 0 && root[e[i][0]] == 0)
      {
        root[e[i][0]] = x;
        q[q2++] = e[i][0];
      }
    }
  }
  for (int i = 1; i <= n; ++i)
  {
    printf("%d\n", root[i]);
  }
  return 0;
}