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.