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D. Vasya And The Matrix

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputNow 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*_{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.

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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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