Budget

Time Limit: 5 Seconds
Memory Limit: 32768 KB
Special Judge

We are supposed to make a budget proposal for this multi-site competition. The
budget proposal is a matrix where the rows represent different kinds of expenses
and the columns represent different sites. We had a meeting about this, some time
ago where we discussed the sums over different kinds of expenses and sums over
different sites. There was also some talk about special constraints: someone mentioned
that Computer Center would need at least 2000K Rials for food and someone from
Sharif Authorities argued they wouldn't use more than 30000K Rials for T-shirts.
Anyway, we are sure there was more; we will go and try to find some notes from
that meeting.

And, by the way, no one really reads budget proposals anyway, so we'll just have
to make sure that it sums up properly and meets all constraints.

**Input**

The first line of the input contains an integer N, giving the number of test
cases. The next line is empty, then, test cases follow: The first line of each
test case contains two integers, m and n, giving the number of rows and columns
(m <= 200, n <= 20). The second line contains m integers, giving the row
sums of the matrix. The third line contains n integers, giving the column sums
of the matrix. The fourth line contains an integer c giving the number of constraints.
The next c lines contain the constraints. There is an empty line after each
test case.

Each constraint consists of two integers r and q, specifying some entry (or
entries) in the matrix (the upper left corner is 1 1 and 0 is interpreted as
"ALL", i.e. 4 0 means all entries on the fourth row and 0 0 means
the entire matrix), one element from the set {<, =, >} and one integer
v, with the obvious interpretation. For instance, the constraint 1 2 > 5
means that the cell in the 1st row and 2nd column must have an entry strictly
greater than 5, and the constraint 4 0 = 3 means that all elements in the fourth
row should be equal to 3.

**Output**

For each case output a matrix of non-negative integers meeting the above constraints
or the string "IMPOSSIBLE" if no legal solution exists. Put one empty
line between matrices.

**Sample Input**

2

2 3

8 10

5 6 7

4

0 2 > 2

2 1 = 3

2 3 > 2

2 3 < 5

2 2

4 5

6 7

1

1 1 > 10

**Sample Output**

2 3 3

3 3 4

IMPOSSIBLE

Source:

**Asia 2003, Tehran (Iran), Preliminary**
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