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.

-----Input-----

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.

-----Output-----

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_{i}1, c_{i}2, ... , 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.

-----Examples-----

Input 2 3 2 9 5 3 13

Output YES 3 4 5 6 7 8

Input 3 3 1 7 6 2 15 12

Output NO