#include <iostream>
#include <time.h>
#include <algorithm>
#define ll long long
#define mod 998244353
using namespace std;
ll bruteForce(ll x, ll y, ll l, ll r) {
ll ans = (x & l) * (y & l);
ll a = l;
for (ll i = l;i <= r;i++) {
ll k = ((x & i) * (y & i));
if (k > ans) {
a = i;ans = k;
}
}
return a;
}
ll vis(ll X, ll Y, ll L, ll R) {
if (min(X, Y) == 0)
return min(L, R);
ll product = 0;
ll ans = ((X & R) | (Y & R));
product = ((R & X) * (R & Y));
ll big = max(X, Y);
ll small = min(X, Y);
if (product == 0)
ans = min(L, R);
while (R > 0) {
int right = (R ^ (R & (R - 1)));
R -= right;
int l = R;
l += (right - 1);// this is the number of interest
// cout << l << "\n";
ll temp = ((l & X) * (l & Y));
if ((temp == product) && l != 0) {
product = temp;
ll a = l & X;
ll b = l & Y;
ll o = (a | b);
ans = min(ans, o);
}
if ((temp > product) && l != 0) {
product = temp;
ll a = l & X;
ll b = l & Y;
ans = (a | b);
}
ll g = l & big;
ll h = l & small;
if ((g == big) && (h == small))
break;
}
// cout << "\n";
return ans;
}
int main() {
int t = 1;
srand(time(0));
while (t) {
ll L = 0;
ll R = rand() % 10000;
ll X = rand() % 10000;
ll Y = rand() % 10000;
cout << "testing for " << X << " " << Y << " " << L << " " << R << "\n";
if (vis(X, Y, L, R) != (bruteForce(X, Y, L, R))) {
cout << "found a conflict!!" << "\n";
cout <<"my code gives"<< vis(X, Y, L, R) << "\n";
cout <<"brute force gives "<< bruteForce(X, Y, L, R) << "\n";
cout << X << " " << Y << " " << L << " " << R << "\n";
t = 0;
}
}
}
