Reindeer Games

Description:

Input:

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2\le n\le 1000$$$; $$$1\le m\le 1000$$$) — the number of reindeer and requirements, respectively.

The second line contains $$$n$$$ integers $$$a_1,\ldots, a_n$$$ ($$$1\le a_i\le 10^9$$$), where $$$a_i$$$ is the current score of reindeer $$$i$$$.

The next $$$m$$$ lines describe the requirements.

The $$$i$$$-th of these lines contains two integers $$$u_i$$$ and $$$v_i$$$ ($$$1\le u_i, v_i\le n$$$; $$$u_i\ne v_i$$$) — the two reindeer of the $$$i$$$-th requirement.

Output:

Print $$$n$$$ integers $$$b_1,\ldots, b_n$$$ ($$$-10^{15}\le b_i\le 10^{15}$$$), where $$$b_i$$$ is the score of the $$$i$$$-th reindeer after all operations.

If there are multiple solutions achieving the minimum number of operations, you may output any.

We can prove that there is always an optimal solution such that $$$|b_i|\le 10^{15}$$$ for all $$$i$$$.

Sample Input:

7 6
3 1 4 9 2 5 6
1 2
2 3
3 4
4 5
5 6
6 7

Sample Output:

1 1 4 4 4 5 6 

Sample Input:

4 6
6 5 8 2
3 1
4 1
3 2
1 2
2 3
3 1

Sample Output:

6 6 6 2 

Sample Input:

10 18
214 204 195 182 180 176 176 172 169 167
1 2
3 2
4 2
5 2
6 2
7 2
8 2
9 2
10 2
6 1
6 2
6 3
6 4
6 5
6 7
6 8
6 9
6 10

Sample Output:

204 204 195 182 180 167 176 172 169 167