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 Lua (Lua 5.3.5) (judge verdict: Accepted)

local n, m = io.read("*n", "*n")
local edge = {}
local pcnt = {}
local len = {}
for i = 1, n do
  edge[i] = {}
  pcnt[i] = 0
  len[i] = 0
end
local rawsrc, rawdst = {}, {}
for i = 1, n - 1 + m do
  local a, b = io.read("*n", "*n")
  table.insert(edge[a], b)
  pcnt[b] = pcnt[b] + 1
  rawsrc[i], rawdst[i] = a, b
end
local tasks = {}
for i = 1, n do
  if pcnt[i] == 0 then
    tasks[1] = i
    break
  end
end
local done = 0
while done < #tasks do
  done = done + 1
  local src = tasks[done]
  local l = len[src]
  local edgesrc = edge[src]
  for i = 1, #edgesrc do
    local dst = edgesrc[i]
    if len[dst] < len[src] + 1 then
      len[dst] = len[src] + 1
    end
    pcnt[dst] = pcnt[dst] - 1
    if pcnt[dst] == 0 then
      table.insert(tasks, dst)
    end
  end
end
local parent = {}
for i = 1, n do
  parent[i] = 0
end
for i = 1, n - 1 + m do
  local src, dst = rawsrc[i], rawdst[i]
  if len[src] + 1 == len[dst] then
    parent[dst] = src
  end
end
print(table.concat(parent, "\n"))