#include <bits/stdc++.h>
#define ll long long
#define sz(x) int(x.size())
#define all(x) x.begin(),x.end()
#define fr first
#define se second
#define pb push_back
using namespace std;
long long collisions(std::vector<long long> x);
bool can(vector<ll>v, vector<ll>u)
{
map<ll,ll>used;
for(auto k:v)
used[k]=1;
for(auto k:u)
if(used[k])
continue;
else
{
used[k]=1;
v.pb(k);
}
return collisions(v);
}
ll calc(ll x, ll y)
{
if(x>y)
swap(x,y);
ll tam=y-x, i;
vector<ll>divs;
for(i=2; i<=sqrt(tam); i++)
{
if(tam%i!=0)
continue;
if(collisions({1+i,1}))
return i;
if(i!=sqrt(tam))
divs.pb(tam/i);
}
while(sz(divs))
{
if(collisions({divs.back()+1,1}))
return divs.back();
divs.pop_back();
}
return tam;
}
const ll maxM=1e9, prim=14009;
//const ll maxM=1e1, prim=3;
int hack(){
ll i, j;
vector<ll>v(prim), u;
iota(v.begin(),v.end(),1);
for(i=((maxM/2)/prim)*prim; i<=maxM+prim; i+=prim)
u.pb(i);
while(sz(v)>1||sz(u)>1)
{
if(sz(v)<sz(u))
swap(v,u);
ll mid=sz(v)/2;
if(can(vector(v.begin(),v.begin()+mid),u))
v.resize(mid);
else
v=vector(v.begin()+mid,v.end());
}
return calc(v[0],u[0]);
}
