We have N (N ≤ 10000) objects, and wish to classify them into several groups by judgement of their resemblance. To simply the model, each object has 2 indexes a and b (a, b ≤ 500). The resemblance of object i and object j is defined by d_ij = |a_i - a_j| + |b_i - b_j|, and then we say i is d_ij resemble to j. Now we want to find the minimum value of X, so that we can classify the N objects into K (K < N) groups, and in each group, one object is at most X resemble to another object in the same group, i.e, for every object i, if i is not the only member of the group, then there exists one object j (i ≠ j) in the same group that satisfies d_ij ≤ X

The first line contains two integers N and K. The following N lines each contain two integers a and b, which describe a object.

A single line contains the minimum X.

 #include<cstdio>

 #include<iostream>

 #include<cmath>

 #include<cstring>

 #include<algorithm>

 #define maxn 100005

 #define inf 1061109567

 using namespace std;

 char ch;

 bool ok;

 void read(int &x){

     for (ok=,ch=getchar();!isdigit(ch);ch=getchar()) if (ch=='-') ok=;

     for (x=;isdigit(ch);x=x*+ch-'',ch=getchar());

     if (ok) x=-x;

 }

 struct Point{

     int x,y,d,id;

 }point[maxn],tmp[maxn];

 bool cmp1(Point a,Point b){

     if (a.x!=b.x) return a.x>b.x;

     return a.y>b.y;

 }

 int calc(Point a,Point b){return abs(a.x-b.x)+abs(a.y-b.y);}

 int n,m,k,ans;

 struct DATA{

     int val,pos;

     void init(){val=inf,pos=-;}

     void update(DATA b){if (val>b.val) val=b.val,pos=b.pos;}

 };

 int d[maxn],cntd;

 struct bit{

     #define lowbit(x) ((x)&(-(x)))

     DATA node[maxn];

     void init(){for (int i=;i<=cntd;i++) node[i].init();}

     void insert(int x,DATA p){for (int i=cntd-x+;i<=cntd;i+=lowbit(i)) node[i].update(p);}

     int query(int x){

         DATA ans; ans.init();

         for (int i=cntd-x+;i;i-=lowbit(i)) ans.update(node[i]);

         return ans.pos;

     }

 }T;

 struct Edge{

     int u,v,c;

 }edge[maxn<<];

 bool cmp2(Edge a,Edge b){return a.c<b.c;}

 void prepare(){

     for (int i=;i<=n;i++) d[i]=point[i].d=point[i].y-point[i].x;

     sort(d+,d+n+),cntd=unique(d+,d+n+)-d-;

     for (int i=;i<=n;i++) point[i].d=lower_bound(d+,d+cntd+,point[i].d)-d;

     sort(point+,point+n+,cmp1),T.init();

     for (int i=;i<=n;i++){

         int u=point[i].id,v=T.query(point[i].d);

         if (v!=-) edge[++m]=(Edge){u,v,calc(tmp[u],tmp[v])};

         T.insert(point[i].d,(DATA){point[i].x+point[i].y,u});

     }

 }

 int fa[maxn];

 int find(int x){return x==fa[x]?fa[x]:fa[x]=find(fa[x]);}

 int main(){

     read(n),read(k);

     for (int i=;i<=n;i++) read(point[i].x),read(point[i].y),point[i].id=i;

     for (int i=;i<=n;i++) tmp[i]=point[i]; prepare();

     for (int i=;i<=n;i++) point[i].x=tmp[i].y,point[i].y=tmp[i].x,point[i].id=i; prepare();

     for (int i=;i<=n;i++) point[i].x=-tmp[i].y,point[i].y=tmp[i].x,point[i].id=i; prepare();

     for (int i=;i<=n;i++) point[i].x=tmp[i].x,point[i].y=-tmp[i].y,point[i].id=i; prepare();

     sort(edge+,edge+m+,cmp2);

     for (int i=;i<=n;i++) fa[i]=i;

     for (int i=,cnt=n;i<=m&&cnt>k;i++) if (find(edge[i].u)!=find(edge[i].v))

         cnt--,ans=max(ans,edge[i].c),fa[find(edge[i].u)]=find(edge[i].v);

     printf("%d\n",ans);

     return ;

 }