Most Distinctive Character

Tira wants to join a multiplayer game with $n$ other players. Every player uses one character, and a character has some features. The game has $k$ features in total, and each character has a subset of them.

The similarity of two characters $A$ and $B$ is counted like this. For each feature $f$, if $A$ and $B$ both have $f$, or if neither of them has $f$, the similarity goes up by $1$.

Tira has no character yet. She wants to build a new character so that the largest similarity between her character and any other character is as small as possible.

Given the characters of the other players, find such a character for Tira. Several characters can reach the smallest possible maximum similarity, and in that case the answer is the one that comes first in lexicographic order.

The first line contains two integers $n$ and $k$ separated by a space. $n$ is the number of players other than Tira, with $1 \le n \le 10^5$, and $k$ is the number of features, with $1 \le k \le 20$.

Each of the next $n$ lines holds one existing character as a string of $k$ digits, each of them $0$ or $1$. A $1$ in position $j$ means the character has the $j$-th feature, and a $0$ means it does not. The same character may appear more than once.

Print Tira's character on one line, in the same format as the input. If several characters give the same smallest maximum similarity, print only the lexicographically smallest of them. Two strings of the same length $k$ are compared position by position from the left, and $0$ comes before $1$ in every position.