Problem:
Score : 300 points

Problem Statement

Snuke loves puzzles.

Today, he is working on a puzzle using S- and c-shaped pieces.
In this puzzle, you can combine two c-shaped pieces into one S-shaped piece, as shown in the figure below:

Snuke decided to create as many Scc groups as possible by putting together one S-shaped piece and two c-shaped pieces.

Find the maximum number of Scc groups that can be created when Snuke has N S-shaped pieces and M c-shaped pieces.

Constraints

1 ≤ N,M ≤ 10^{12}

Input

The input is given from Standard Input in the following format:

N M

Output

Print the answer.

Sample Input 1

1 6

Sample Output 1

2

Two Scc groups can be created as follows:

Combine two c-shaped pieces into one S-shaped piece

Create two Scc groups, each from one S-shaped piece and two c-shaped pieces

Sample Input 2

12345 678901

Sample Output 2

175897

Solution in LuaJIT (2.0.4) (judge verdict: Wrong Answer)

function main()
  local input = string.gmatch(io.read(), "[^ ]+")
  local n = tonumber(input())
  local m = tonumber(input())

  local convert = math.floor((m - 2*n)/2)
  if convert > 0 then
    n = n + math.floor(convert/2)
    m = m - convert
  end

  if n < 2*m then
    print(n)
  else
    print(math.floor(m/2))
  end
end

main()