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


def get_root(A):
    res = [A]
    search = [A]
    visit = [False for i in range(N)]
    while(len(search) > 0):
        now = search.pop()
        if visit[now-1]:
            continue
        visit[now-1] = True
        for a in ans[now-1]:
            if a == 0:
                continue
            if visit[a-1]:
                continue
            res.append(a)
            search.append(a)
    return set(res)


N, M = map(int, input().split(" "))
AB = [list(map(int, input().split(" "))) for i in range(N+M-1)]

AB = sorted(AB, key=itemgetter(1))
count = 1
before = -1
temp = [AB[0][0]]
ans = [[0, ] for i in range(N)]
before = AB[0][1]
for a, b in AB[1:]:
    if before != b:
        ans[before-1] = temp
        temp = [a, ]
        before = b
    else:
        temp.append(a)

if len(temp) > 0:
    ans[-1] = (temp)

new_ans = []
for i, each_ans in enumerate(ans):
    if len(each_ans) == 1:
        new_ans.append(each_ans[0])
        continue
    for a in each_ans:
        if set(each_ans) & get_root(a) == set(each_ans):
            new_ans.append(a)
            break

for line in new_ans:
    print(line)