A11890 | Vasya And The Matrix

Now Vasya is taking an exam in mathematics. In order to get a good mark, Vasya needs to guess the matrix that the teacher has constructed!

Vasya knows that the matrix consists of $n$ rows and $m$ columns. For each row, he knows the xor (bitwise excluding or) of the elements in this row. The sequence $a_{1},a_{2},...,a_{n}$ denotes the xor of elements in rows with indices $1$ , $2$ , ..., $n$ , respectively. Similarly, for each column, he knows the xor of the elements in this column. The sequence $b_{1},b_{2},...,b_{m}$ denotes the xor of elements in columns with indices $1$ , $2$ , ..., $m$ , respectively.

Help Vasya! Find a matrix satisfying the given constraints or tell him that there is no suitable matrix.

The first line contains two numbers $n$ and $m (2<=n,m<=100)$ — the dimensions of the matrix.

The second line contains $n$ numbers $a_{1},a_{2},...,a_{n} (0<=a_{i}<=10^{9})$ , where $a_{i}$ is the xor of all elements in row $i$ .

The third line contains $m$ numbers $b_{1},b_{2},...,b_{m} (0<=b_{i}<=10^{9})$ , where $b_{i}$ is the xor of all elements in column $i$ .

If there is no matrix satisfying the given constraints in the first line, output "NO".

Otherwise, on the first line output "YES", and then $n$ rows of $m$ numbers in each $c_{i1},c_{i2},...\ ,c_{im} (0<=c_{ij}<=2·10^{9})$ — the description of the matrix.

If there are several suitable matrices, it is allowed to print any of them.