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: Accepted)

N, M = [int(_) for _ in input().split()]
AB = [[int(_) for _ in input().split()] for i in range(N - 1 + M)]

from collections import defaultdict

nodes = list(range(1, N + 1))
edges = defaultdict(set)
rev_edges = defaultdict(set)

for a, b in AB:
    edges[a].add(b)
    rev_edges[b].add(a)

#print(vs)
#print(ws)

def TopologicalSort(nodes, edges, rev_edges):
    '''
    nodes     ... Node[]
    edges     ... Dict[From Node](To Node)
    rev_edges ... Dict[To Node](From Node)
    '''
    rev_edges_num = dict((n, len(rev_edges[n])) for n in nodes)
    L = []
    S = [n for n in nodes if not rev_edges_num[n]]
    while S:
        n = S.pop()
        L.append(n)
        for m in edges[n]:
            rev_edges_num[m] -= 1
            if not rev_edges_num[m]:
                S.append(m)
    
    # プロコン用なのでエラーチェックはしない

    return L

L = TopologicalSort(nodes, edges, rev_edges)

nrank = dict((n, r) for r, n in enumerate(L))

for n in range(1, N + 1):
    r = 0
    if rev_edges[n]:
        r = sorted(rev_edges[n], key=lambda x:nrank[x], reverse=True)[0]
    print(r)