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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

hash = Hash.new{|h,k| h[k] = []}
inv_hash = [] #Hash.new{|h,k| h[k] = []}

nm = gets.chomp.split(" ").map(&:to_i)

for i in 0..nm[0]-2+nm[1]
  a = gets.chomp.split(" ").map(&:to_i)
  hash[a[0]] << a[1]
  inv_hash << a[1] #[a[1]] << a[0]
end

NODE_WEIGHT = Array.new(nm[0]+1)

start = (hash.keys - inv_hash.uniq)[0]

queue = [[start, 0, 0]]

while queue != []
  k = queue.pop
  next if NODE_WEIGHT[k[0]] && NODE_WEIGHT[k[0]][0] >= k[1]
  NODE_WEIGHT[k[0]] = [k[1], k[2]] if !NODE_WEIGHT[k[0]] || NODE_WEIGHT[k[0]][0] < k[1]
  hash[k[0]].each do |i|
    #if !NODE_WEIGHT[i] || NODE_WEIGHT[k[0]][0] < k[1]
    #NODE_WEIGHT[i] = [k[1]+1, k[0]]
    queue.push [i, k[1] + 1, k[0]]
  end
end

for i in 1..nm[0]
  puts NODE_WEIGHT[i][1]
end