// Generated code

​

using System;

using System.Linq;

using System.Numerics;

using NUnit.Framework;

​

public class KeyGenerator

{

    public static string GenerateKey(string code, long hint)

    {

        // Input Validation

        if (string.IsNullOrEmpty(code) || !code.All(char.IsDigit))

        {

            return "INVALID KEY";

        }

​

        if (code.Any(c => c == '0'))

        {

            return "INVALID KEY";

        }

​

        if (hint < 1)

        {

            return "INVALID KEY";

        }

​

        BigInteger currentKey = BigInteger.Parse(code);

        BigInteger maxKey = BigInteger.Parse("9".PadLeft(code.Length + 2, '9')); // Limit search to reasonable length

​

        while (currentKey <= maxKey)

        {

            string keyString = currentKey.ToString();

​

            if (keyString.Contains('0'))

            {

                currentKey++;

                continue;

            }

​

            long product = 1;

            foreach (char digitChar in keyString)

            {

                product *= (digitChar - '0');

            }

​

            if (product % hint == 0)

            {

                return keyString;

            }

​

            currentKey++;

        }

​

        return "INVALID KEY";

    }

​

    public static void Main(string[] args)

    {

        // Example Usage (can be modified)

        string code1 = "1234";

        long hint1 = 256;

        Console.WriteLine($"Code: {code1}, Hint: {hint1}, Key: {GenerateKey(code1, hint1)}");

​

        string code2 = "12355";

        long hint2 = 50;

        Console.WriteLine($"Code: {code2}, Hint: {hint2}, Key: {GenerateKey(code2, hint2)}");

​

        string code3 = "11111";

        long hint3 = 26;

        Console.WriteLine($"Code: {code3}, Hint: {hint3}, Key: {GenerateKey(code3, hint3)}");

​

        string code4 = "10";

        long hint4 = 320;

        Console.WriteLine($"Code: {code4}, Hint: {hint4}, Key: {GenerateKey(code4, hint4)}");

​

        string code5 = "12";

        long hint5 = 1968750;

        Console.WriteLine($"Code: {code5}, Hint: {hint5}, Key: {GenerateKey(code5, hint5)}");

    }

}