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: Wrong Answer)


from collections import deque
def inpl(): return list(map(int, input().split()))

N, M = inpl()
G = {i:[] for i in range(N)}
X = [0]*(N)
searched = [0]*(N)
pairents = [-1]*N

for _ in range(N-1+M):
    a, b = inpl()
    G[a-1].append(b-1)
    X[b-1] += 1

q = X.index(0)

Q = deque([q])
while Q:
    p = Q.popleft()
    for q in G[p]:
        if not searched[q]:
            searched[q] = searched[p] + 1
            Q.append(q)            
        elif searched[q] <= searched[p]:
            searched[q] = searched[p] + 1

for a in range(N):
    for b in G[a]:
        if searched[b] == searched[a] + 1:
            pairents[b] = a
for p in pairents:
    print(p+1)