Starting at cell $(0, 0)$, you want to reach the destination cell at coordinates $(`row`, `column`)$ given by destination $= [`row`, `column`]$.

From any cell $(r, c)$, you can make one of the following moves:

• Move down to $(r + 1, c)$, represented by the character 'V'.

• Move right to $(r, c + 1)$, represented by the character 'H'.

A valid sequence of instructions consists of exactly row vertical moves 'V' and column horizontal moves 'H'.

There may be multiple valid instruction sequences that reach destination. When ordered lexicographically, 'H' comes before 'V'.

Given an array destination and an integer k, return the $k^{ ext{th}}$ lexicographically smallest instruction string to reach destination.

Constraints:

• destination.length $= 2$

• destination $= [`row`, `column`]$

• $1 \leq$ row, column $\leq 15$

• $1 \leq$ k $\leq ext{nCr}(`row` + `column`, `row`)$, where $ ext{nCr}(a, b)$ denotes $a$ choose $b$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.