Team Composition- Programmers and Mathematicians.cpp

// https://codeforces.com/contest/1611/problem/B
/*

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*/

#include <bits/stdc++.h>

using namespace std;

#define fi          first
#define se          second
#define pb          push_back
#define mp          make_pair
#define all(x)      x.begin(), x.end()
#define ll          long long
#define pll         pair<ll, ll>
#define vll         vector<long long>
#define mll         map<ll, ll>
#define inf         1e18
#define gcd(a, b)   __gcd(a, b)
#define range(a,b)  substr(a,b-a+1)
#define setbits(x)  __builtin_popcountll(x)
#define zrobits(x)  __builtin_ctzll(x)
#define fori(a, n)  for (ll i = a; i < n; i++)
#define forj(a, n)  for (ll j = a; j < n; j++)
#define fork(a, n)  for (ll k = a; k < n; k++)
#define print(x)    for (auto i : x) {cout << i << " ";}
#define FIO         ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
mt19937             rng(chrono::steady_clock::now().time_since_epoch().count());

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

int main()
{
    FIO;

    #ifndef ONLINE_JUDGE
    //remove this piece of code when this has to be submitted in kickstart, coding ninjas
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    //freopen is used to associate a file with stdin or stdout stream in C++
    #endif

    ll t;
    cin >> t;
    while (t--) {
        ll a, b;
        cin >> a >> b;
        if (a == 0 || b == 0 || (a + b) < 4)
            cout << 0 << "\n";
        else if (a == b)
            cout << a / 2 << "\n";
        else if (min(a, b) * 3 <= max(a, b))
            cout << min(a, b) << "\n";
        else {
            ll l = 1, r = 1e9;
            while (l <= r) {
                ll mid = (l + r) / 2;
                if (min(a, b) - mid >= max(a, b) - 3 * mid)
                    r = mid - 1;
                else
                    l = mid + 1;
            }
            ll ans = l;
            if (a < b) {
                a -= l;
                b -= 3 * l;
                if (min(a, b) < 0) {
                    ans--;
                    a += 1;
                    b += 3;
                }
            }
            else {
                a -= 3 * l;
                b -= l;
                if (min(a, b) < 0) {
                    ans--;
                    a += 3;
                    b += 1;
                }
            }
            cout << ans + min(a, b) / 2 << "\n";
        }
    }

    return 0;
}