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: Time Limit Exceeded)

from operator import itemgetter

n, m = map(int, input().split())
number = [[-1, -1] for i in range(n)]
tree = [[] for i in range(n)]
for i in range(n - 1 + m):
    a, b = map(int, input().split())
    tree[b - 1].append(a)
nagasa = []
for i in range(n):
    nagasa.append((i, len(tree[i])))
nagasa = sorted(nagasa, key=itemgetter(1))
nokori = set()
while True:
    for j in range(n):
        i = nagasa[j][0]
        if number[i][0] != -1:
            continue
        if len(tree[i]) == 1:
            if number[tree[i][0] - 1][1] == -1:
                nokori.add(i)
                continue
            number[i] = [tree[i][0], number[tree[i][0] - 1][1] + 1]
        elif len(tree[i]) == 0:
            number[i] = [0, 0]
        else:
            kari = []
            m = 0
            flag = 0
            for k in tree[i]:
                if number[k - 1][1] == -1:
                    nokori.add(i)
                    flag = 1
                    break
                kari.append((k, number[k - 1][1] + 1))
                m = max(m, number[k - 1][1] + 1)
            if flag:
                continue
            for k in kari:
                if k[1] == m:
                    number[i] = k
                    break
        nokori.discard(i)
    if len(nokori) == 0:
        break
for i in number:
    print(i[0])