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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

# 有効グラフ上で、近道に当たる点はすべて余計な辺
# ある点に入ってくる最も距離が長い辺のみが有効となる
# 一番距離が長い人版ダイクストラやってみる
# 入力のあった頂点を記録することで、入力の無かった頂点を根とみなせる

import sys
readline = sys.stdin.readline

N,M = map(int,readline().split())
G = [[] for i in range(N)]
grandparent = set(range(N))
for i in range(N - 1 + M):
  a,b = map(int,readline().split())
  G[a-1].append(b-1)
  grandparent -= {b - 1}

start = list(grandparent)[0]
import heapq

# 距離, 頂点, 親
q = [(0, start, -1)]
heapq.heapify(q)

# ans[頂点] = (到達コスト,親)
ans = [(-1, -1) for i in range(N)]
while q:
  dist, v, parent = heapq.heappop(q)
  dist = -dist
  if ans[v][0] >= dist:
    continue
  ans[v] = (dist, parent)
  for child in G[v]:
    heapq.heappush(q,(-(dist + 1), child, v))
    
for a in ans:
  print(a[1] + 1)