#include <bits/stdc++.h>

#define rep(i,s,n) for(int i = int(s); i < int(n); i++)
#define rrep(i,s,n) for(int i = int(n) - 1; i >= int(s); i--)
#define all(v) (v).begin(), (v).end()

using ll = long long;
using ld = long double;
using ull = unsigned long long;

template<class T>
bool chmin(T &a, T b) {
    if(a <= b) return false;
    a = b;
    return true;
}

template<class T>
bool chmax(T &a, T b) {
    if(a >= b) return false;
    a = b;
    return true;
}

using namespace std;

int main() {
	ll n, m; cin >> n >> m;

	auto check = [&](ll t) -> bool {
		ll a = max((ll)0, n - 3 * t);
		ll c = max((ll)0, m - 3 * t);
		if (a + c <= t){
			return true;
		}else{
			return false;
		}
	};

	ll ub = 1e9;
	ll lb = 0;
	while(ub - lb > 1){
		ll t = (ub + lb) / 2;
		if (check(t)){
			ub = t;
		}else{
			lb = t;
		}
	}

	cout << ub * 2 - 1 << '\n';
}