## OPTM - Optimal Marks

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You are given an undirected graph G(V, E). Each vertex has a mark which is an integer from the range [0..231 – 1]. Different vertexes may have the same mark.

For an edge (u, v), we define Cost(u, v) = mark[u] xor mark[v].

Now we know the marks of some certain nodes. You have to determine the marks of other nodes so that the total cost of edges is as small as possible.

### Input

The first line of the input data contains integer T (1 ≤ T ≤ 10) - the number of testcases. Then the descriptions of T testcases follow.

First line of each testcase contains 2 integers N and M (0 < N <= 500, 0 <= M <= 3000). N is the number of vertexes and M is the number of edges. Then M lines describing edges follow, each of them contains two integers u, v representing an edge connecting u and v.

Then an integer K, representing the number of nodes whose mark is known. The next K lines contain 2 integers u and p each, meaning that node u has a mark p. It’s guaranteed that nodes won’t duplicate in this part.

### Output

For each testcase you should print N lines integer the output. The Kth line contains an integer number representing the mark of node K. If there are several solutions, you have to output the one which minimize the sum of marks. If there are several solutions, just output any of them.

### Example

```Input:
1
3 2
1 2
2 3
2
1 5
3 100

Output:
5
4
100
```

hide comments gy1323119614: 2016-07-27 02:43:39 bzoj 2400 Samiul: 2014-08-13 07:35:35 If you are having trouble solving this, try COCONUTS first moustafa maher: 2013-09-19 07:36:13 NO prudhvi: 2013-09-01 16:46:49 can the solution for the first case be: 5 1 100

 Added by: Thanh-Vy Hua Date: 2006-05-05 Time limit: 1.407s Source limit: 10000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ERL JS-RHINO NODEJS PERL6 VB.NET Resource: Guo HuaYang