Problem Statement

There is a grid with $H$ rows and $W$ columns, where the cell at the $i$-th row from the top and $j$-th column from the left is denoted as $(i,j)$. The grid has a hole only in cell $(r,c)$. We will tile all cells without a hole using several tiles. You are given non-negative integers $N$ and $M$ such that $H \times W=L \times (N+M)+1$. A tile of $1$ row and $L$ columns is called a horizontal tile, and a tile of $L$ rows and $1$ column is called a vertical tile. Determine whether there exists a way to tile using exactly $N$ horizontal tiles and $M$ vertical tiles without rotation, and also show one such way if it exists. For details on the output format and more precise conditions, check the output section.

Solve $T$ test cases for each input file.

Constraints

• $1 \leq T \leq 5$
• $1 \leq H \leq 1000$
• $1 \leq W \leq 1000$
• $2 \leq H \times W$
• $2 \leq L \leq 1000$
• $0 \leq N$
• $0 \leq M$
• $1 \leq r \leq H$
• $1 \leq c \leq W$
• $H \times W=L \times (N+M)+1$
• The sum of $N+M$ over all test cases is at most $6\times 10^5$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
case_1
case_2
\vdots
case_T

Each case is given in the following format:

H W L N M r c

Output

Output the answers in the following format:

output_1
output_2
\vdots
output_T

Here, $output_t$ represents the output for the $t$-th test case. For each case, if it is possible to tile satisfying the conditions, let $(A_i,B_i)$ be the leftmost cell covered by the $i$-th horizontal tile and $(C_j,D_j)$ be the topmost cell covered by the $j$-th vertical tile, and output in the following format:

Yes
A_1 B_1
A_2 B_2
\vdots
A_N B_N
C_1 D_1
C_2 D_2
\vdots
C_M D_M

More precisely, output integer sequences $A=(A_1,A_2,\dots,A_N),B=(B_1,B_2,\dots,B_N)$ of length $N$ and $C=(C_1,C_2,\dots,C_M),D=(D_1,D_2,\dots,D_M)$ of length $M$ that satisfy all of the following conditions:

• The union of $\{(A_i,B_i+l)\mid i=1,2,\dots,N,\;l=0,1,\dots,L-1\}$, $\{(C_j+l,D_j)\mid j=1,2,\dots,M,\;l=0,1,\dots,L-1\}$, and $\{(r,c)\}$ equals $\{(h,w)\mid h=1,2,\dots,H,\;w=1,2,\dots,W\}$.

Note that due to the constraint $H \times W=L \times (N+M)+1$, when this condition holds, tiles do not overlap with each other.

If it is impossible to satisfy the conditions, output No.