Need a script (preferably in Node.js) to generate and solve puzzle(kakuro) -- 3

Need a developer or a mathematician to create an algorithm/API for generating a Kakuro puzzle and finding the solution. Puzzle size varies between 5 to 20 and there should be an option to set difficulty. The parameters are width, height, difficulty and number of puzzles to be generated. IMPORTANT: The puzzle must have ONLY ONE solution not multiple solutions. Node.js example : [login to view URL]('/kakuro', async (req, res) => { const { width, height, amount, difficulty } = [login to view URL] ..... const result = await [login to view URL](width, height, amount, difficulty) // here kakuro class is needed ..... } The result will be the puzzle itself, its solution and the difficulty info. You can check these for more information on the puzzle : [login to view URL] [login to view URL] Please feel free to apply even if you're not a programmer but can provide algorithm assistance. Here are some questions for you. 1. How would you implement the requirement for solution uniqueness? 2. What can be the factors for the puzzle difficulty? 3. How long do you think this will take? 4. Where you able to find any reference code?