Gardening

Azusa, the witch of the highlands, wants to do a fun activity with her friend Laika: gardening. They want to make a rectangular garden $N$ meters tall by $M$ meters wide. The garden is divided into $1$ meter by $1$ meter squares. The question is: what flowers should they plant?

Laika has found $K$ different types of flowers. Azusa and Laika will plant one type of flower in each $1$ meter by $1$ meter square. Furthermore, for aesthetic reasons, the garden must satisfy the following constraints:

1. Each flower type must appear at least once in the garden.
2. For any two squares where the same flower type is planted, a path between them where all the intermediate squares have the same type of flower must exist. For example, the following gardens are not allowed:

3. Any square must have exactly two adjacent squares planted with the same type of flower. For example, the following gardens are not allowed:

Note that, in the previous constraints, two squares are “adjacent” if and only if they share a common edge (not merely a corner); and a path is a sequence of adjacent squares.

You are given $T$ different values for $N, M$ and $K$. Help Azusa and Laika create gardens that satisfy the conditions for each test case — or, tell them that it is impossible to do this.

Input data

The first line of the input contains the integer $T$. Afterwards, $T$ lines follow, each describing a test case. Each test case consists of three integers $N, M$ and $K$.

Output data

Output the answers for each test case in order. For a test case, if no solution exists, output NO on a single line. Otherwise, first output YES on a single line, and then output $N \cdot M$ integers arranged in $N$ lines and $M$ columns describing the required garden. The lines and columns of the output correspond to the lines and columns of the garden, with each integer corresponding to a $1$ meter by $1$ meter square. The integers represent the types of flowers planted in the squares, where the types are indexed from $1$ to $K$. If there are multiple correct solutions you may output any of them.

Restrictions

• $1 \leq T \leq 100 \ 000$
• $1 \leq N, M \leq 200 \ 000$
• $1 \leq K \leq N \cdot M$
• Let $S$ equal the sum of $N \cdot M$ for all the test cases in a file for which an answer exists (i.e. where the output is not NO).
• $S \leq 200 \ 000$

Examples

stdin

5
2 2 2
2 2 1
4 4 4
4 4 2
4 6 3

stdout

NO
YES
1 1
1 1
YES
1 1 2 2
1 1 2 2
3 3 4 4
3 3 4 4
YES
1 1 1 1
1 2 2 1
1 2 2 1
1 1 1 1
YES
1 1 1 1 1 1
1 2 2 3 3 1
1 2 2 3 3 1
1 1 1 1 1 1

Explanations

For the first test case, we note that no $2$ by $2$ garden with $2$ types of flowers is possible. Thus we output NO. The other gardens are pictured below: