Krishnakant is standing at $(0,0)$ in the Cartesian plane. He wants to go to the point $(x,y)$ in the same plane using only horizontal and vertical moves of $1$ unit. There are many ways of doing this, and he is writing down all such ways. Each way comprises of few ${H}$ moves and few $V}$ moves. i.e. moves in horizontal and vertical direction respectively. For example, if Krishnakant wants to go to point $(2,2)$ from point $(0,0)$, ${HVHV}$ is one of the possible ways.

Given the value of ${K}$, he wants to know lexicographically $K^{{th}}$ smallest way of going to $(x,y)$ from $(0,0)$.

Input Format

The first line contains an integer ${T}$ , i.e., number of test cases.

Next ${T}$ lines will contain integers ${x}$,$y$ and ${K}$.

Output Format

For each test case, print lexicographically $K^{{th}}$ smallest path.

Constraints

$1\leq T\leq1000000$

$1\leq x\leq10$

$1\leq y\leq10$

$0\leq K<\text{number of paths}$

Sample Input

2
2 2 2
2 2 3

Sample Output

HVVH
VHHV

Explanation

All the paths of going to $(2,2)$ from $(0,0)$ in lexicographically increasing order:

$0.HHVV$

$1.HVHV$

$2.HVVH$

$3.VHHV$

$4.VHVH$

$5.VVHH$

见题面

见题面