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: Wrong Answer)

# import numpy as np

import sys
sys.setrecursionlimit(200000)


N, M = list(map(int, input().split(" ")))

A, B = [], []
to = [[] for i in range(N)]

for _ in range(N + M - 1):
    q = input()
    a, b = list(map(int, q.split(" ")))
    A.append(a)
    B.append(b)
    to[a - 1].append(b - 1)


class Node:
    def __init__(self):
        self.parent = set()
        self.children = set()
        self.deep = 0
        self.res = 0


nodes = [Node() for _ in range(N + 1)]

for a, b in zip(A, B):
    nodes[b].parent.add(a)
    nodes[a].children.add(b)

root_num = int(list(set(A) - set(B))[0])


def traverse(root):
    # for p in root.parent:
    #     root.anc = root.anc.union(nodes[p].anc)
    #     root.anc = root.anc.union(nodes[p].parent)
    for c in root.children:
        if nodes[c].deep == 0:
            nodes[c].deep = max(nodes[c].deep, root.deep + 1)
            traverse(nodes[c])


traverse(nodes[root_num])

for i in range(1, N + 1):
    deep = nodes[i].deep
    if deep == 0:
        nodes[i].res = 0
    for p in nodes[i].parent:
        if nodes[p].deep == deep - 1:
            nodes[i].res = p
            break

for i in range(1, N + 1):
    print(nodes[i].res)


# for i in range(1, N + 1):
#     rm = []
#     for p in nodes[i].parent:
#         if p in nodes[i].anc:
#             rm.append(p)
#     for p in rm:
#         nodes[i].parent.remove(p)
#         nodes[p].children.remove(i)

# for i in range(1, N + 1):
#     if len(nodes[i].parent) == 0:
#         print(0)
#     else:
#         print(list(nodes[i].parent)[0])