Kevin wants a "perfect matrix" with ~N~ rows and ~M~ columns.

He has certain expectations for some matrix ~K~ that he considers perfect.

He has a desired integer range for each element of ~K~, as well as a desired integer range for each row sum and column sum.

More formally, given ~2~ other ~N \times M~ matrices ~L~ and ~R~, and matrices ~A~ and ~B~ of dimensions ~N \times 2~ and ~M \times 2~ respectively, all of the following conditions must hold:

• ~L_{ij} \le K_{ij} \le R_{ij}~ for all (~1 \le i \le N, 1 \le j \le M)~
• ~A_{i1} \le \sum_{j=1}^{M} K_{ij} \le A_{i2}~ for all ~(1 \le i \le N)~
• ~B_{j1} \le \sum_{i=1}^{N} K_{ij} \le B_{j2}~ for all ~(1 \le j \le M)~

Help Kevin find any perfect matrix or determine that it is impossible to do so.

Constraints

~1 \le N, M \le 1000~

~0 \le L_{ij} \le R_{ij} \le 10^6~

~0 \le A_{i1} \le A_{i2} \le 10^9~

~0 \le B_{j1} \le B_{j2} \le 10^9~

Input Specification

The first line of input contains integers ~N~ and ~M~.

The next ~N~ lines of input each contain ~M~ space-separated integers representing the matrix ~L~, the minimum values of each element.

The next ~N~ lines of input each contain ~M~ space-separated integers representing the matrix ~R~, the maximum values of each element.

The next ~N~ lines of input each contain ~2~ space-separated integers representing the matrix ~A~, the minimum and maximum sums of each row.

The next ~M~ lines of input each contain ~2~ space-separated integers representing the matrix ~B~, the minimum and maximum sums of each column.

Output Specification

Output ~N~ lines of ~M~ space-separated integers representing any perfect matrix that satisfies Kevin or report that it is impossible to do so by outputting -1.

Sample Input

2 2
3 0
0 3
3 9
9 3
5 5
1 6
6 9
0 9

Sample Output

3 2
3 3

Explanation for Sample

In the example above, this is the only matrix that Kevin will consider perfect.