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 <cmath>
#include <vector>
#include <algorithm>

using namespace std;

long long n, m;

bool f(long long need) {

    long long nn = n;
    long long mm = m;

    if (nn < need) {
        long long cur = need - nn;
        mm -= 2 * cur;
        nn += cur;
    }

    return (mm >= 2 * need);
}

int main(void) {

    cin >> n >> m;
    long long l = 0;
    long long r = 1e13;

    while (r - l > 1) {
        long long m = (l + r) / 2;

        if (f(m)) {
            l = m;
        } else {
            r = m;
        }
    }

    cout << l << endl;
    return 0;
}