Restore the Tree

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.

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.

Examples

Input

3 1 1 2 1 3 2 3

Output

0 1 2

Input

6 3 2 1 2 3 4 1 4 2 6 1 2 6 4 6 6 5

Output

6 4 2 0 6 2

inputFormat

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}

outputFormat

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.

Examples

Input

3 1 1 2 1 3 2 3

Output

0 1 2

Input

6 3 2 1 2 3 4 1 4 2 6 1 2 6 4 6 6 5

Output

6 4 2 0 6 2

样例

6 3
2 1
2 3
4 1
4 2
6 1
2 6
4 6
6 5

6
4
2
0
6
2

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