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 Rust (1.15.1) (judge verdict: Runtime Error)

#[test]
fn check_solve() {
    println!("input:\n6\nooxoox\noutput:\n{}\n", solve("6\nooxoox\n"));
    println!("input:\n3\noox\noutput:\n{}\n", solve("3\noox\n"));
    println!(
        "input:\n10\noxooxoxoox\noutput:\n{}\n",
        solve("10\noxooxoxoox\n")
    );
}
fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);
    let n: usize = sc.read();
    let s: Vec<_> = sc.get().chars().collect();

    for &(a0, a1) in [('S', 'S'), ('S', 'W'), ('W', 'S'), ('W', 'W')].iter() {
        let mut a = Vec::with_capacity(n+1);
        a.push(a0);
        a.push(a1);
        for i in 2..n+1 {
            let lie = a[i-1] == 'W';
            if (s[i-1] == 'o') ^ lie {
                let nxt = a[i-2];
                a.push(nxt);
            } else if a[i-2] == 'S' {
                a.push('W');
            } else {
                a.push('S');
            }
        }
        if a[0] == a[n] {
            a.pop();
            return a.into_iter().collect();
        }
    }

    format!("-1\n")
}
fn main() {
    let mut buf = String::new();
    use std::io::{Read, Write};
    std::io::stdin().read_to_string(&mut buf).unwrap();
    std::io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}
struct Scanner<'a>(std::str::SplitWhitespace<'a>);
impl<'a> Scanner<'a> {
    fn from_str(src: &str) -> Scanner {
        Scanner(src.split_whitespace())
    }
    fn get(&mut self) -> &str {
        self.0.next().unwrap()
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.get().parse().ok().unwrap()
    }
}