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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>
#include <random>
#include <ctime>
#include <map>
#include <queue>
#include <functional>

using namespace std; using ll=long long; using P=pair<ll,ll>; const int INF=1e9; const ll LNF=1e18;

int main(){
  ll n,m; cin>>n>>m;
  ll ok = 0, ng = 1e12;
  while(ng - ok > 1) {
    ll md = (ng + ok) / 2;
    ll t = n, u = m;
    if (md > t) u-=(md-t)*2, t=md;
    //cout << md << " " << u << endl;
    if (u >= md * 2) ok = md;
    else ng = md;
  }
  cout<<ok<<endl;
}