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)

n,m=gets.split.map(&:to_i)
kiarray=Array.new(n).map{Array.new(2).map{Array.new}}
(n-1+m).times{
    parent,child=gets.split.map(&:to_i)
    kiarray[parent-1][1].push(child)
    kiarray[child-1][0].push(parent)
}

root=0
n.times{|k|
    if kiarray[k][0]==[]
        root=k+1
        break
    end
}

nisecount=0
que=[root]

while nisecount<m
    shift = que.shift
   children=kiarray[shift-1][1]

   ll=children.length
   index=0
   ll.times{
        value=children[index]
        if !kiarray[value-1][0][1]
            que.push(value)
            index+=1
         else
            nisecount+=1
            kiarray[shift-1][1].delete(value)
            kiarray[value-1][0].delete(shift)
        end
   }
end

kiarray.map.with_index{|value,index|
    if  index==root-1
        puts 0
    else
        puts value[0][0]
    end
}