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: Accepted)

import sys
# from heapq import heappop, heappush
from collections import deque
sys.setrecursionlimit(10 ** 9)
input = sys.stdin.readline

N, M = map(int, input().split())
check_lst = [0] * N
lst = [[] for _ in range(N)]
for _ in range(N + M - 1):
    A, B = map(int, input().split())
    A -= 1
    B -= 1
    lst[A].append(B) #無向グラフの作成
    check_lst[B] += 1 #その点に入って来る辺が何本あるかを数える

n = check_lst.index(0) #入って来る辺が無いとき、その頂点がスタート
ans = [0] * N #答えのリスト
que = deque()
q_append = que.append
q_append(n) #スタートをqueに入れる
q_left = que.popleft
while que:
    v = q_left()
    for v2 in lst[v]: #頂点vから出る辺について走査
        check_lst[v2] -= 1
        if check_lst[v2] == 0: #最後に出てきたものだけ考える
            q_append(v2)
            ans[v2] = v + 1

print (*ans, sep = '\n')