Matrix

You are given two $m \times n$ matrices $A$ and $B$. Matrix $B$ comes from matrix $A$ by row-addition operations and column-subtraction operations. One row-addition operation adds 1 to every entry of a row, and one column-subtraction operation subtracts 1 from every entry of a column.

Find the numbers of row-addition operations $r_1, \dots, r_m$ applied to row 1 through row $m$ of $A$ so that all of the following hold.

• There exist numbers of column-subtraction operations $c_1, \dots, c_n$ applied to column 1 through column $n$ of $A$ such that these row and column operations turn $A$ into $B$.
• Every count is between 0 and 9 inclusive, that is $0 \le r_i \le 9$ for $i = 1, \dots, m$ and $0 \le c_j \le 9$ for $j = 1, \dots, n$.
• The value $r_1 \dots r_m$, read as one integer, is as small as possible.

The answer is $r_1$ through $r_m$ concatenated in order. If $B$ cannot be obtained from $A$ within these limits, the answer is $-1$.

The first line contains two integers $m$ and $n$ separated by a space ($1 \le m \le 100$, $1 \le n \le 100$).

The next $m$ lines give matrix $A$, from row 1 to row $m$. Each of these lines contains $n$ integers separated by single spaces. The next $m$ lines give matrix $B$ in the same format.

Every entry of both matrices is an integer between $-1000$ and $1000$ inclusive.

Print one line.

If the transformation is possible, print $r_1$ through $r_m$ concatenated in order as a digit string of length $m$, keeping any leading zeros. Otherwise print $-1$.