Problem:
Score : 200 points

Problem Statement

Square1001 has seen an electric bulletin board displaying the integer 1.
He can perform the following operations A and B to change this value:

Operation A: The displayed value is doubled.

Operation B: The displayed value increases by K.

Square1001 needs to perform these operations N times in total.
Find the minimum possible value displayed in the board after N operations.

Constraints

1 \leq N, K \leq 10

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
K

Output

Print the minimum possible value displayed in the board after N operations.

Sample Input 1

4
3

Sample Output 1

10

The value will be minimized when the operations are performed in the following order: A, A, B, B.

In this case, the value will change as follows: 1 → 2 → 4 → 7 → 10.

Sample Input 2

10
10

Sample Output 2

76

The value will be minimized when the operations are performed in the following order: A, A, A, A, B, B, B, B, B, B.

In this case, the value will change as follows: 1 → 2 → 4 → 8 → 16 → 26 → 36 → 46 → 56 → 66 → 76.

By the way, this contest is AtCoder Beginner Contest 076.

Solution in C# (Mono-csc 3.5.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
  class Program
  {
    static void Main(string[] args)
    {
      ABC076.B();
    }
    class ABC078
    {
      public static void A()
      {
        var X = Read.Str();
        var Y = Read.Str();
        Console.WriteLine(X == Y ? "=" : (X.CompareTo(Y) > 0 ? ">" : "<"));
      }
      public static void B()
      {
        var X = Read.Int();
        var Y = Read.Int();
        var Z = Read.Int();
        int max = 0;
        for (int i = 1; i < 100000; ++i)
        {
          if (Y * i + Z * (i + 1) <= X)
          {
            max = i;
          }
          else { break; }
        }
        Console.WriteLine(max);
      }
    }
    class ABC077
    {
      public static void A()
      {
        var C1 = Read.Str();
        var C2 = Read.Str();
        Console.WriteLine(C1 == new string(C2.Reverse().ToArray()) ? "YES" : "NO");
      }
      public static void B()
      {
        var N = Read.Long();
        long max = 0;
        for(long i=1; ; ++i)
        {
          if (i * i <= N)
          {
            max = i * i;
          }
          else { break; }
        }
        Console.WriteLine(max);
      }
    }
    class ABC076
    {
      public static void A()
      {
        var R = Read.Int();
        var G = Read.Int();
        Console.WriteLine(G * 2 - R);
      }
      public static void B()
      {
        var N = Read.Int();
        var K = Read.Int();
        int current = 1;
        for(int i = 0; i < N; ++i)
        {
          if (current > K)
          {
            current += K;
          }
          else
          {
            current *= 2;
          }
        }
        Console.WriteLine(current);
      }
      public static void C()
      {
        var S = Read.Str();
        var T = Read.Str();
        string ans = "";
        for(int i = 0; i <= S.Length - T.Length; ++i)
        {
          bool ok = true;
          for(int j = 0; j < T.Length; ++j)
          {
            var s = S[i + j];
            var t = T[j];
            if (s == '?' || s == t) { } else { ok = false; break; }
          }
          if (ok)
          {
            char[] x = new char[S.Length];
            for(int j = 0; j < S.Length; ++j)
            {
              if (S[j] == '?')
              {
                if (i <= j && j < i + T.Length)
                {
                  x[j] = T[j - i];
                }
                else
                {
                  x[j] = 'a';
                }
              }
              else
              {
                x[j] = S[j];
              }
            }
            var xs = new string(x);
            if (xs.CompareTo(ans) < 0 || ans == "")
            {
              ans = xs;
            }
          }
        }
        Console.WriteLine(ans=="" ? "UNRESTORABLE" : ans);
      }
      public static void D()
      {

      }
    }

    class Util
    {
      public static T[,] Gen<T>(int r, int c, T v)
      {
        var matrix = new T[r, c];
        for (int i = 0; i < r; ++i)
        {
          for (int j = 0; j < c; ++j)
          {
            matrix[i, j] = v;
          }
        }
        return matrix;
      }
      public static long[] ASum(long[] array)
      {
        var res = new long[array.Length + 1];
        for (int i = 0; i < array.Length; ++i)
        {
          res[i + 1] = res[i] + array[i];
        }
        return res;
      }
      public static long[,] ASum(long[,] matrix)
      {
        var N = matrix.GetLength(0);
        var M = matrix.GetLength(1);
        var res = new long[N + 1, M + 1];
        for(int i = 0; i < N; ++i)
        {
          for(int j = 0; j < M; ++j)
          {
            res[i + 1, j + 1] = res[i, j + 1] + res[i + 1, j] - res[i, j] + matrix[i, j];
          }
        }
        return res;
      }
      public static Dictionary<T, long> Frequency<T>(T[] array)
      {
        var dict = new Dictionary<T, long>();
        foreach (var a in array)
        {
          if (!dict.ContainsKey(a)) { dict.Add(a, 0); }
          dict[a]++;
        }
        return dict;
      }
      public static bool IsPrime(long x)
      {
        var fact = Factorize(x);
        return fact.Count == 1 && fact.Values.ElementAt(0) == 1;
      }
      public static Dictionary<long, int> Factorize(long x)
      {
        var dict = new Dictionary<long, int>();
        long minp = 2;
        while (x > 1)
        {
          bool ok = false;
          for (long p = minp; p * p <= x; ++p)
          {
            if (x % p == 0)
            {
              if (!dict.ContainsKey(p))
              {
                dict.Add(p, 0);
              }
              dict[p]++;
              minp = p;
              x /= p;
              ok = true;
              break;
            }
          }
          if (!ok)
          {
            if (!dict.ContainsKey(x)) { dict.Add(x, 0); }
            dict[x]++;
            break;
          }
        }
        return dict;
      }
      public static HashSet<int> GenPrimes(int max)
      {
        var primes = new HashSet<int>(Enumerable.Range(2, max - 1));
        for(int i = 2; i <= max; ++i)
        {
          if (primes.Contains(i))
          {
            for(int j=2; ; ++j)
            {
              if (i * j > max) { break; }
              primes.Remove(i * j);
            }
          }
        }
        return primes;
      }
      public static T[,] Transpose<T>(T[,] matrix)
      {
        var r = matrix.GetLength(0);
        var c = matrix.GetLength(1);
        var matrixOut = new T[c, r];
        for (int i = 0; i < r; ++i)
        {
          for (int j = 0; j < c; ++j)
          {
            matrixOut[j, i] = matrix[i, j];
          }
        }
        return matrixOut;
      }

      public class PriorityQueue<T> where T : IComparable
      {
        private IComparer<T> _comparer = null; private bool _isAsc = true; private T[] _heap; private int _sz = 0;
        public PriorityQueue(int maxSize, IComparer<T> comparer) { _heap = new T[maxSize]; _comparer = comparer; }
        public PriorityQueue(int maxSize, bool isAsc = true) { _heap = new T[maxSize]; _isAsc = isAsc; }
        private int Compare(T x, T y) { if (_comparer != null) { return _comparer.Compare(x, y); } return _isAsc ? x.CompareTo(y) : y.CompareTo(x); }
        public void Push(T x) { var i = _sz++; while (i > 0) { var p = (i - 1) / 2; if (Compare(_heap[p], x) <= 0) { break; } _heap[i] = _heap[p]; i = p; } _heap[i] = x; }
        public T Pop() { T ret = _heap[0]; T x = _heap[--_sz]; int i = 0; while (i * 2 + 1 < _sz) { int a = i * 2 + 1; int b = i * 2 + 2; if (b < _sz && Compare(_heap[b], _heap[a]) < 0) { a = b; } if (Compare(_heap[a], x) >= 0) { break; } _heap[i] = _heap[a]; i = a; } _heap[i] = x; return ret; }
        public int Count() { return _sz; }
        public T Peek() { return _heap[0]; }
        public bool Contains(T x) { for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true; return false; }
      }
      public class MyTuple<T1, T2> : IComparable where T1 : IComparable<T1>
      {
        public readonly T1 Item1; public readonly T2 Item2;
        public MyTuple(T1 item1, T2 item2) { Item1 = item1; Item2 = item2; }
        public int CompareTo(object obj) { return Item1.CompareTo(((MyTuple<T1, T2>)obj).Item1); }
      }
      public static long[] DijkstraDense(long[,] adj, int N, int start)
      {
        long INF = (long)1e18;
        var dist = Enumerable.Range(0, N + 1).Select(i => INF).ToArray();
        var queue = new PriorityQueue<MyTuple<long, int>>(N + N * N + 100);
        dist[start] = 0;
        queue.Push(new MyTuple<long, int>(0, start));
        while (queue.Count() > 0)
        {
          var kvp = queue.Pop();
          var d = kvp.Item1; var v = kvp.Item2;
          if (dist[v] < d) { continue; }
          for (int i = 0; i < N; ++i)
          {
            if (i == v) { continue; }
            var newV = i;
            var newD = dist[v] + adj[v, i];
            if (newD < dist[newV])
            {
              dist[newV] = newD;
              queue.Push(new MyTuple<long, int>(newD, newV));
            }
          }
        }
        return dist;
      }
    }

    static class Read
{
static Queue<string> queue = new Queue<string>();
static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
public static ulong[] ULongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToUInt64(s)).ToArray(); }
public static string[] StrN() { return Console.ReadLine().Split(' '); }
public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
public static long[,] LongMatrix(int r, int c) { var mat = new long[r, c]; for (int i = 0; i < r; ++i) { var x = Read.LongN(); for (int j = 0; j < c; ++j) { mat[i, j] = x[j]; } } return mat; }
public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
{
Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
        for (int i = 0; i < M; ++i) { var ab = Read.IntN(); if (!dict[ab[0]].Contains(ab[1])) { dict[ab[0]].Add(ab[1]); } if (!isDirectional && !dict[ab[1]].Contains(ab[0])) { dict[ab[1]].Add(ab[0]); } }
        return dict;
}
public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
{
Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>(); for (int i = 0; i <= N; ++i) { dict.Add(i, new Dictionary<int, long>()); }
for (int i = 0; i < M; ++i) { var ab = Read.IntN(); dict[ab[0]].Add(ab[1], ab[2]); dict[ab[1]].Add(ab[0], ab[2]); }
return dict;
}
}
    }
}