Problem:
Score: 100 points

Problem Statement

There is a train going from Station A to Station B that costs X yen (the currency of Japan).

Also, there is a bus going from Station B to Station C that costs Y yen.

Joisino got a special ticket. With this ticket, she can take the bus for half the fare if she travels from Station A to Station B by train and then travels from Station B to Station C by bus.

How much does it cost to travel from Station A to Station C if she uses this ticket?

Constraints

1 \leq X,Y \leq 100

Y is an even number.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

If it costs x yen to travel from Station A to Station C, print x.

Sample Input 1

81 58

Sample Output 1

110

The train fare is 81 yen.

The train fare is 58 ⁄ 2=29 yen with the 50% discount.

Thus, it costs 110 yen to travel from Station A to Station C.

Sample Input 2

4 54

Sample Output 2

31

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

def is_valid_row?(row)
  (row.size-1).times do |j|
    return false if row[j]=='1' and row[j+1]=='1'
  end
  true
end

def valid_rows(w)
  (2**(w-1)).times.map do |i|
    sprintf("%0#{w-1}b0", i)  # last bit is always zero
  end.select do |row|
    is_valid_row?(row)
  end
end

$dp_count_valid_rows = {}

def count_valid_rows(w, ini, dx)
  key = "#{ini},#{dx}"
  if $dp_count_valid_rows[key]
    return $dp_count_valid_rows[key]
  end

  if dx == 0
    ans = valid_rows(w).count do |row|
      row[ini] == '0' and row[ini-1] == '0'
    end
  elsif dx == 1
    ans = valid_rows(w).count do |row|
      row[ini] == '1'
    end
  elsif dx == -1
    ans = valid_rows(w).count do |row|
      row[ini-1] == '1'
    end
  else
    ans = 0
  end
  $dp_count_valid_rows[key] = ans
  return $dp_count_valid_rows[key]
end

$dp_count_correct_amida = {}

D = 1000000007
  

def count_correct_amida(h, w, ini, dest)
  key = "#{h},#{ini},#{dest}"
  if $dp_count_correct_amida[key]
    return $dp_count_correct_amida[key]
  end

  if ini >= w or ini < 0
    ans = 0
  elsif h == 0
    ans = (dest == ini ? 1 : 0)
  else
    n0 = count_valid_rows(w, ini, 0) * count_correct_amida(h-1, w, ini, dest)
    n1 = count_valid_rows(w, ini, 1) * count_correct_amida(h-1, w, ini+1, dest)
    n2 = count_valid_rows(w, ini, -1) * count_correct_amida(h-1, w, ini-1, dest)
    ans = (n0 + n1 + n2) % D
  end
  $dp_count_correct_amida[key] = ans
  $dp_count_correct_amida[key]
end

H,W,K = readline.chomp.split.map(&:to_i)
puts count_correct_amida(H, W, 0, K-1)