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 Python (3.4.3) (judge verdict: Runtime Error)

from collections import deque

n, m = map(int, input().split())
parent = {i:[] for i in range(n)}
child = {i:[] for i in range(n)}
root = [i for i in range(n)]
for _ in range(n-1+m):
    a,b = map(int, input().split())
    child[a-1].append(b-1)
    if b-1 in root:
        root.remove(b-1)

root = root[0]

true_parent = {}
distance = {i:0 for i in range(n)}

def find_parent(node):
    node_parent = parent[node]
    if true_parent[node]:
        return true_parent[node]
    elif len(node_parent)==1:
        true_parent[node] = node_parent[0]
        distance[node] = distance[node_parent[0]]+1
        return node_parent[0]
    else:
        mx = 0
        for p in node_parent:
            tmp = find_parent(p)
            if mx < distance[tmp]:
                mx = distance[tmp]
                mxp = p
        true_parent[node] = p
        distance[node] = distance[p]+1
        return p

for i in range(n):
    if i == root:
        print(0)
    else:
        print(find_parent(i)+1)