Lawson is a magic swordsman with $k$ kinds of magic attributes $v_1, v_2, v_3, \dots, v_k$. Now Lawson is faced with $n$ monsters and the $i$-th monster also has $k$ kinds of defensive attributes $a_{i,1}, a_{i,2}, a_{i,3}, \dots, a_{i, k}$. If $v_1\geq a_{i,1}$ and $v_2\geq a_{i,2}$ and $v_3\geq a_{i,3}$ and $\dots$ and $v_k\geq a_{i, k}$, 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 $j = 1, 2, 3, \dots, k$.
Now we want to know how many monsters Lawson can kill at most and how much Lawson's magic attributes can be maximized.

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 $k$ ($1\leq n \leq 10^5, 1\leq k \leq 5$).
The second line has $k$ non-negative integers (initial magic attributes) $v_1, v_2, v_3, \dots, v_k$.
For the next $n$ lines, the $i$-th line contains $2k$ non-negative integers $a_{i,1}, a_{i,2}, a_{i,3}, \dots, a_{i, k}, b_{i,1}, b_{i,2}, b_{i,3}, \dots, b_{i, k}$.
It's guaranteed that all input integers are no more than $10^9$ and $v_j + \displaystyle\sum_{i=1}^n b_{i,j} \leq 10^9$ for $j = 1, 2, 3, \dots, k$.

It is guaranteed that the sum of all n $\leq 5 \times 10 ^ 5$.
The input data is very large so fast IO (like `fread`) is recommended.

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 $v_1', v_2', v_3', \dots, v_k'$ and the $i$-th integer means maximum of the $i$-th magic attibute.