# HDU 6396 Swordsman

• 2018-08-16
• 26
• 0

## Description:

Lawson is a magic swordsman with k kinds of magic attributes v_1,v_2,v_3,…,v_k. Now Lawson is faced with n monsters and the i-th monster also has k kinds of defensive attributes a_{i,1},a_{i,2},a_{i,3},…,a_{i,k}. If v_1≥a_{i,1} and v_2≥a_{i,2} and v_3≥a_{i,3} and … and v_k≥a_{i,k}, Lawson can kill the i-th monster (each monster can be killed for at most one time) and get EXP from the battle, which means v_j will increase b_{i,j} for j=1,2,3,…,k.
Now we want to know how many monsters Lawson can kill at most and how much Lawson’s magic attributes can be maximized.

## Input:

There are multiple test cases. The first line of input contains an integer T, indicating the number of test cases. For each test case:

The first line has two integers n and k (1≤n≤10^5,1≤k≤5).

The second line has k non-negative integers (initial magic attributes) v_1,v_2,v_3,…,v_k.

For the next n lines, the i-th line contains 2k non-negative integers a_{i,1},a_{i,2},a_{i,3},…,a_{i,k},b_{i,1},b_{i,2},b_{i,3},…,b_{i,k}.

It’s guaranteed that all input integers are no more than 10^9​ and v_{j}+\sum_{i=1}^{n}{b_{i,j}}\le 10^{9}​forj=1,2,3,…,k​.

It is guaranteed that the sum of all n ≤5×10^5.
The input data is very large so fast IO (like fread) is recommended.

## Output:

For each test case:
The first line has one integer which means the maximum number of monsters that can be killed by Lawson.
The second line has k integers v′_1,v′_2,v′_3,…,v′_k and the i-th integer means maximum of the i-th magic attibute.

1
4 3
7 1 1
5 5 2 6 3 1
24 1 1 1 2 1
0 4 1 5 1 1
6 0 1 5 3 1

3
23 8 4

## Hint:

For the sample, initial V = [7, 1, 1]
① kill monster #4 (6, 0, 1), V + [5, 3, 1] = [12, 4, 2]
② kill monster #3 (0, 4, 1), V + [5, 1, 1] = [17, 5, 3]
③ kill monster #1 (5, 5, 2), V + [6, 3, 1] = [23, 8, 4]
After three battles, Lawson are still not able to kill monster #2 (24, 1, 1)
because 23 < 24.