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 (2.7.6) (judge verdict: Time Limit Exceeded)

# -*- coding: utf-8 -*-
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys

def s():
    return raw_input().strip()
def n():
    return int(raw_input())
def d():
    return float(raw_input())

def ls():
    return raw_input().strip().split()
def ln():
    return map(int, raw_input().strip().split())
def ld():
    return map(float, raw_input().strip().split())

def fs():
    return [raw_input().strip() for i in xrange(input())]
def fn():
    return [int(raw_input().strip()) for i in xrange(input())]
def fd():
    return [float(raw_input().strip()) for i in xrange(input())]

sys.setrecursionlimit(300000)

N, M = ln()

parent = collections.defaultdict(list)
child = collections.defaultdict(list)

for i in xrange(N - 1 + M):
    a, b = ln()
    parent[b].append(a)
    child[a].append(b)

top = 1
while parent[top]:
    top = parent[top][0]

unique_root = [0] * (N + 1)
v_depth = [0] * (N + 1)
def f(cur, depth, prev):
    if v_depth[cur] < depth or prev == 0:
        unique_root[cur] = prev
        v_depth[cur] = depth
        for c in child[cur]:
            f(c, depth + 1, cur)

f(top, 0, 0)

print '\n'.join(map(str, unique_root[1:]))