PROJECT EULER #16

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2¹⁵ = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.

What is the sum of the digits of the number 2¹⁰⁰⁰?

using System;
using System.Collections.Generic;

namespace ProjectEuler
{
   class Program
   {
       static void Main(string[] args)
       {
           //Problem 16
           DateTime start = DateTime.Now;
           //This is about doubling 2, 999 times
           //This number is too big for the system types in C#
           int carry=0, sum=0;
           List<int> a = new List<int>(){2};
           List<int> b = new List<int>();
           for (int i = 2; i <= 1000;i++ )
           {
               foreach (int j in a)
               {
                   int c = j*2 + carry;

                   if (c > 9)
                   {
                       c = c - 10;
                       carry = 1;
                   }
                   else
                   {
                       carry = 0;
                   }
                   b.Add(c);
               }
               if (b.Count == a.Count && carry == 1)
                   b.Add(1);
               carry = 0;
               a.Clear();
               foreach (int j in b)
               {
                   a.Add(j);
               }
               b.Clear();
           }
           foreach(int j in a)
           {
               sum += j;
           }
           TimeSpan time = DateTime.Now-start;
           Console.WriteLine("{0}\nThis took {1}", sum, time);
           Console.ReadKey();
       }
   }
}