Description

Construct an $n\times m$ $01$ matrix such that the number of $1$s in each row is $r_1,r_2,\ldots,r_n$, and the number of $1$s in each column is $c_1,c_2,\ldots,c_m$.

Among all valid matrices, the result should be lexicographically smallest. When comparing two matrices in lexicographical order, first compare the first row; if they are equal, compare the second row; and so on.

Input Format

The first line contains two integers $n,m$.

The second line contains $n$ integers $r_1,r_2,\ldots,r_n$.

The third line contains $m$ integers $c_1,c_2,\ldots,c_m$.

Output Format

Output an $n\times m$ matrix.

2 3
2 1 
1 0 2 

101
001

Hint

For $100\%$ of the testdata, $n,m\le 100$.

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