Shortest Subsequence Given Operations

using System;
using System.Collections.Generic;

/// <summary>
/// I can't figure out how to backtrack and print the solution
/// </summary>

namespace _678.Problem_10
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = 5;
            int m = 16;
            int sum = n;

            Queue<int> subsetFinder = new Queue<int>();
            subsetFinder.Enqueue(n);
            while (sum < m)
            {
                sum = subsetFinder.Dequeue();
                // Console.Write(sum + " ");

                if ((sum * 2) <= m && !subsetFinder.Contains(sum * 2))
                {
                    subsetFinder.Enqueue(sum * 2);
                }
                if ((sum + 2) <= m && !subsetFinder.Contains(sum + 2))
                {
                    subsetFinder.Enqueue(sum + 2);
                }
                if ((sum + 1) <= m && !subsetFinder.Contains(sum + 1))
                {
                    subsetFinder.Enqueue(sum + 1);
                }
            }
        }
    }
}