4939. NP Transformation

输入格式

The first line consists of two integers — $n$ and $m$ ($1\le n,m\le 1000$), denoting the number of bitsets and the length of bitsets.

In the following $n$ lines, each line consists of $m$ bits per line, denoting the list of bitsets $A$.

In the following $n$ lines, each line consists of $m$ bits per line, denoting the list of bitsets $B$.

The input is guaranteed that $B$ is NP transformed by $A$.

输出格式

The first line consists of $m$ integers, denoting the permutation of $A$.

The second line consists of $m$ bits, denoting the negation of $A$.

2 4
0000
0111
0101
1011

2 3 4 1
0 1 0 1

提示

After the permutation $2,3,4,1$ of A, the bitset list is $0000,1110$.

And then after the negation $0,1,0,1$ of A, the bitset list is $0101,1011$.