K - Koa the Koala

Languages: C, C++, Java, Python, ... (details)

There are $n$ cats and $n$ dogs, each numbered from $1$ to $n$. From their locations each of them can look at other cats and dogs. In particular the following is happening:

1. Every cat looks exactly at $a$ dogs (i.e. $a$ distinct integers from $1$ to $n$).
2. Every dog looks exactly at $b$ cats (i.e. $b$ distinct integers from $1$ to $n$).

Something really bad will happen if a cat and a dog are looking at each other at the same time, so Koa the Koala will help to sort out this situation. She has to determine whether it is possible to arrange which are the target animals each animal is looking at, in such a way that:

• (1.) and (2.) are satisfied
• there isn't a pair of cat and dog looking at each other, that is: there can't exists integers $i$ and $j$ $(1 \le i, j \le n)$ such that the cat $i$ is looking at dog $j$ and dog $j$ is looking at cat $i$.

Help her!

Input

First line of the input contains one integer $t$ ($1 \le t \le 100$), the number of test cases. Then $t$ test cases follow.

The only line of each test case contains three integers $n$, $a$ and $b$ ($1 \le n \le 100$  ;  $1 \le a, b \le n)$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $100$ ($\sum n \le 100$).

Output

For each test case:

Print "Yes" or "No" (without quotes), depending on whether such arrangement exists.

• Then exactly $n$ lines must follow, indicating how cats are looking at dogs.
• The $i$-th ($1 \le i \le n$) line must consist of exactly $a$ distinct integers $w_1, w_2, \ldots, w_a$ ($1\le w_i \le n$) indicating that cat $i$ looks at dogs $w_1, w_2, \ldots, w_a$. These integers can be in any order.
• Then exactly $n$ lines must follow, indicating how dogs are looking at cats.
• The $i$-th ($1 \le i \le n$) line must consist of exactly $b$ distinct integers $m_1, m_2, \ldots, m_b$ ($1\le m_i\le n$), indicating that dog $i$ looks at cats $m_1, m_2, \ldots, m_b$. These integers can be in any order.

If there are many possible arrangements print any.

Sample test(s)

Input
4 3 1 2 5 4 4 7 7 6 2 1 1
Output
Yes 1 2 3 2 3 1 3 1 2 No No Yes 1 2 2 1