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 (1.42.0) (judge verdict: Runtime Error)

#![allow(unused_imports)]
#![allow(clippy::many_single_char_names)]
#![allow(clippy::suspicious_arithmetic_impl)]

// using Rust(1.42.0)
// My Library Repo is at "https://github.com/Loptall/prcn_lib"
// check available crates on AtCoder at "https://atcoder.jp/contests/language-test-202001"

/*
    AtCoder Language Update 2020204 お疲れ様でした! 有難いです
*/

// from std...
use std::cmp::{max, min, Ordering};
use std::collections::{BTreeMap, BTreeSet, HashMap, HashSet, VecDeque};
use std::mem::swap;
use std::ops::*;
use std::usize::{MAX, MIN};
use std::{i128, i16, i32, i64, i8, isize, u128, u16, u32, u64, u8, usize};

// Dep crates are...
use itertools::*;
use itertools_num::*;
use lazy_static::lazy_static;
use maplit::{btreemap, btreeset, hashmap, hashset};
use num_bigint::{BigInt, BigUint};
use num_integer::{binomial, gcd, lcm, Integer};
use permutohedron::Heap;
use petgraph::unionfind::UnionFind;
use proconio::{fastout, input, is_stdin_empty, marker::*};
use rand::random;

/// `l`が`pred`に対し`true`, `r`が`pred`に対し`false`を返す時
/// `l`と`r`の中間の値のうちで最後に`pred`を満たすものを返す
pub fn binary_search<T, F>(l: T, r: T, pred: F) -> T
where
    T: Add<Output = T> + Div<Output = T> + PartialEq + From<u8> + Copy,
    F: Fn(T) -> bool,
{
    let mut l = l;
    let mut r = r;
    let two = T::from(2u8);

    loop {
        let m = (l + r) / two;
        if l == m || r == m {
            break l;
        }
        if pred(m) {
            l = m;
        } else {
            r = m;
        }
    }
}

/// vの要素について最初に現れたval以上の要素のインデックスを返す
pub fn lower_bound<T: PartialOrd>(v: &[T], val: &T) -> usize {
    (binary_search(-1i64, v.len() as i64, |i| v[i as usize] < *val) + 1) as usize
}

/// vの要素について最初に現れたvalより大きい要素のインデックスを返す
pub fn upper_bound<T: PartialOrd>(v: &[T], val: &T) -> usize {
    (binary_search(-1i64, v.len() as i64, |i| v[i as usize] <= *val) + 1) as usize
}

// code...
// #[fastout]
fn main() {
    input! {
        n: usize, m: usize,
    }

    let v = (n..=(n + m / 2)).map(|x| (x, n * 2 + m - 2 * x)).collect::<Vec<_>>();
    let ans = binary_search(0, v.len(), |x| v[x].0 * 2 <= v[x].1);

    println!("{}", ans + n);
}