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: Time Limit Exceeded)

from heapq import heappush, heappop, heapify

def main():
    n, m = map(int, input().split())
    edges = [[] for _ in range(n)]
    isRoot = [True] * n
    for _ in range(n - 1 + m):
        a, b = map(int, input().split())
        a -= 1
        b -= 1
        edges[a].append(b)
        isRoot[b] = False

    for i in range(n):
        if isRoot[i]:
            root = i
            break
    INF = 10 ** 20
    stack = [(0, root, -1)]
    heapify(stack)
    height = [-INF] * n
    parent = [None] * n
    def search(stack):
        score, node, par = stack.pop()
        if -score > height[node]:
            height[node] = -score
            parent[node] = par
            for to in edges[node]:
                heappush(stack,(score - 1, to, node))

    while stack:
        search(stack)

    for i in range(n):
        print(parent[i] + 1)

main()