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 <bits/stdc++.h>
using namespace std;

using lint = long long;

lint s, c;

lint f(lint x) {
    return min(s+x, (c-2*x)/2);
}

int main() {
    cin >> s >> c;

    lint l = 0, r = 1e12;

    while (r-l>2) {
        lint m1 = (l*2+r)/3, m2 = (l+2*r)/3;

        if (f(m1) < f(m2)) l = m1;
        else r = m2;
    }

    lint ans = 0;

    for (lint i=l; i<=r; i++) {
        ans = max(ans, f(i));
    }

    cout << ans << '\n';
}