# USACO : Arithmetic Progressions

```
/*
PROG: ariprog
LANG: C++
*/

#include &lt;bits/stdc++.h&gt;

#define pii             pair &lt;int,int&gt;
#define sc              scanf
#define pf              printf
#define Pi              2*acos(0.0)
#define ms(a,b)         memset(a, b, sizeof(a))
#define pb(a)           push_back(a)
#define MP              make_pair
#define db              double
#define ll              long long
#define EPS             10E-10
#define ff              first
#define ss              second
#define sqr(x)          (x)*(x)
#define D(x)            cout&lt;&lt;#x &quot; = &quot;&lt;&lt;(x)&lt;&lt;endl
#define VI              vector &lt;int&gt;
#define DBG             pf(&quot;Hi\n&quot;)
#define MOD             100007
#define MAX             10000
#define CIN             ios_base::sync_with_stdio(0); cin.tie(0)
#define SZ(a)           (int)a.size()
#define sf(a)           scanf(&quot;%d&quot;,&amp;a)
#define sfl(a)          scanf(&quot;%lld&quot;,&amp;a)
#define sff(a,b)        scanf(&quot;%d %d&quot;,&amp;a,&amp;b)
#define sffl(a,b)       scanf(&quot;%lld %lld&quot;,&amp;a,&amp;b)
#define sfff(a,b,c)     scanf(&quot;%d %d %d&quot;,&amp;a,&amp;b,&amp;c)
#define sfffl(a,b,c)    scanf(&quot;%lld %lld %lld&quot;,&amp;a,&amp;b,&amp;c)
#define loop(i,n)       for(int i=0;i&lt;n;i++)
#define REP(i,a,b)      for(int i=a;i&lt;=b;i++)
#define TEST_CASE(t)    for(int z=1;z&lt;=t;z++)
#define PRINT_CASE      printf(&quot;Case %d: &quot;,z)
#define all(a)          a.begin(),a.end()
#define intlim          2147483648
#define inf             1000000
#define ull             unsigned long long

using namespace std;

/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

//int Set(int N,int pos){return N=N | (1&lt;&lt;pos);}
//int reset(int N,int pos){return N= N &amp; ~(1&lt;&lt;pos);}
//bool check(int N,int pos){return (bool)(N &amp; (1&lt;&lt;pos));}
/*------------------------------------------------*/

int n,m;

bool present[300000];

int main()
{
freopen(&quot;ariprog.in&quot;,&quot;r&quot;,stdin);
freopen(&quot;ariprog.out&quot;,&quot;w&quot;,stdout);
int maxx=INT_MIN;
cin&gt;&gt;n&gt;&gt;m;
for(int i=0; i&lt;=m; i++) for(int j=0; j&lt;=m; j++) present[i*i+j*j]=1,maxx=max(maxx,i*i+j*j);
vector&lt;int&gt;v;
REP(i,0,maxx) if(present[i]) v.pb(i);

vector&lt;pii&gt;ans;

int l=SZ(v);

for(int i=0; i&lt;l; i++)
for(int j=i+1; j&lt;l; j++)
{
int dis=v[j]-v[i];
int k;
int sum=v[i]+dis;
for(k=0; k&lt;n-2; k++)
{
sum+=dis;
if(!present[sum] || sum&gt;2*m*m)
{
break;
}
}
if(k==n-2)
ans.pb(MP(dis,v[i]));
}
sort(all(ans));
if(SZ(ans))
loop(i,SZ(ans)) cout&lt;&lt;ans[i].ss&lt;&lt;&quot; &quot;&lt;&lt;ans[i].ff&lt;&lt;endl;
else
cout&lt;&lt;&quot;NONE&quot;&lt;&lt;endl;
return 0;
}

```