//chockolateman credit
#include<bits/stdc++.h>
#include "hack.h"
using namespace std;
const long long S = 27380;
const long long N = 1000000000;
vector<long long> xf, xs, xf1, xf2, xs1, xs2, y, di;
long long diff, nd;
int hack(){
xf.clear();
for(long long i=1; i <= S; ++i) xf.push_back(i);
xs.clear();
for(long long i=S*(N/2LL/S); i <= N+S; i += S) xs.push_back(i);
while ((int)xf.size() > 1 || (int)xs.size() > 1) {
if ((int)xf.size() <= (int)xs.size()) {
int m = (int)xs.size();
xs1.clear();
for (int i=0; i < m/2; ++i) xs1.push_back(xs[i]);
xs2.clear();
for (int i=m/2; i < m; ++i) xs2.push_back(xs[i]);
y.clear();
for (auto el : xf) y.push_back(el);
for (auto el : xs1) y.push_back(el);
if (collisions(y) != 0) xs = xs1;
else xs = xs2;
}
else {
int m = (int)xf.size();
xf1.clear();
for (int i=0; i < m/2; ++i) xf1.push_back(xf[i]);
xf2.clear();
for (int i=m/2; i < m; ++i) xf2.push_back(xf[i]);
y.clear();
for (auto el : xf2) y.push_back(el);
for (auto el : xs) y.push_back(el);
if (collisions(y) != 0) xf = xf2;
else xf = xf1;
}
}
diff = llabs(xs[0]-xf[0]);
di.clear();
nd = diff;
for (long long d=2LL; d*d <= diff; ++d) {
while (nd % d == 0LL) {
di.push_back(d);
nd /= d;
}
}
if (nd > 1) di.push_back(nd);
sort(di.begin(), di.end());
for (auto d : di) {
diff /= d;
if (collisions({1, diff+1}) == 0) diff *= d;
}
return diff;
}
