//SIXIANG
#include <iostream>
#include <cmath>
#define int long long
#define MAXN 100000
#define QWQ cout << "QWQ" << endl;
using namespace std;
int cdiv(int n, int m) {
	if(n % m == 0) return n / m;
	else return n / m + 1;
}
signed main() {
	int T; cin >> T;
	while(T--) {
		int a, b; cin >> a >> b;
		if(a < b) {
			int o = cdiv(b, a) - 2;
			if(!o) {
				cout << a + (b - a) / 2 << endl;
				continue;
			}
			cout << b - (b - o * a) / 2 << endl;
		}
		else if(a == b) cout << a << endl;
		else cout << a + b << endl;
	}
} 

awa 布吉岛怎么 hack qwq