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: Wrong Answer)

import collections

N,M = map(int,input().split())
AB = []

for i in range(N-1+M):
    a,b = map(int,input().split())
    AB.append((b, a))

dic = collections.Counter(list(range(1,N+1)))

AB = sorted(AB)
tmp = []

ind = 0
for i in range(1,N+1):
    tmp2 = []
    num = 0
    while ind < N - 1 + M and  AB[ind][0] == i:
        tmp2.append(AB[ind][1])
        ind += 1
        num += 1
    tmp.append((num,i,tmp2))

tmp = sorted(tmp)

ans = [0 for _ in range(N+1)]

i = 0
while tmp[i][0] <= 1:
    tar = tmp[i][1]
    if tmp[i][0] == 0:
        ans[tar] = 0
        dic[tar] = 0
    else:
        ans[tar:tar+1] = tmp[i][2][0:1]
        dic[tar] = -1
    i += 1

check = i
while max(dic.values()) == 1:
    i = check
    while i < N:
        tar = tmp[i][1]

        for j in range(tmp[i][0]):
            tar2 = tmp[i][2][j]

            length = 0
            if dic[tar2] <= 0:
                if length < abs(dic[tar2]):
                    length = abs(dic[tar2])
                    ans[tar] = tar2
                    dic[tar] = -length

        i += 1

for a in ans[1:]:
    print(a)