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: Accepted)

from sys import setrecursionlimit
setrecursionlimit(10 ** 9)

n, m = [int(i) for i in input().split()]
A = [[int(i) for i in input().split()] for j in range(n + m - 1)]

T = [[] for i in range(n+1)]
RT = [set() for i in range(n+1)]

for a, b in A:
    T[a].append(b)
    RT[b].add(a)

D = [0] * (n+1)
P = [0] * (n+1)
used = [0] * (n+1)

def dfs(p, i, depth):
    if used[i]:
        return None
    D[i] = depth
    P[i] = p
    used[i] = True
    for t in tuple(T[i]):
        RT[t].remove(i)
    for t in tuple(T[i]):
        if not RT[t]:
            dfs(i, t, depth+1)

def root(i):
    if not RT[i]:
        return i
    return root(tuple(RT[i])[0])

dfs(0, root(1), 1)
for p in P[1:]:
    print(p)