Topical

Benson the Rabbit is attending pilot school.

He has $n$ modules to complete, numbered from $1$ to $n$. There are $k$ topics in flying, numbered from $1$ to $k$. Benson is new to flying, so his knowledge starts at zero in every topic.

Each module has a knowledge requirement. To complete module $i$, Benson needs at least $r[i][j]$ knowledge in each topic $j$. Completing module $i$ gives him $u[i][j]$ more knowledge in each topic $j$.

Formally, let $p[j]$ be Benson's knowledge in topic $j$. Initially, $p[j] = 0$ for all $j$. He can complete module $i$ only if $p[j] \ge r[i][j]$ for every topic $j$. After he completes module $i$, $p[j]$ increases by $u[i][j]$ for each topic $j$.

Benson may complete the modules in any order, but he may complete each module at most once. Find the maximum number of modules he can complete.

The first line contains two space-separated integers $n$ and $k$.

The next $n$ lines describe the requirements. The $i$-th of these lines contains $k$ space-separated integers $r[i][1], r[i][2], \dots, r[i][k]$.

The following $n$ lines describe the gains. The $i$-th of these lines contains $k$ space-separated integers $u[i][1], u[i][2], \dots, u[i][k]$.

Print one integer, the maximum number of modules Benson can complete.

$1 \le n, k \le 10^6$

$n \cdot k \le 10^6$

$0 \le u[i][j], r[i][j] \le 10^9$ for all $1 \le i \le n$ and $1 \le j \le k$.