using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
using System.Threading;
using System.Runtime.CompilerServices;
using System.Diagnostics;
static class Program{
	const long inf=long.MaxValue>>1;
	const int mod=998244353;
	static (int y,int x)[] h;
	static (int y,int x)[] g;
	static Sc sc=new Sc();
	static void Main(){
		Pt pt=new Pt(Solve);
		pt.Sm();
	}
	static void Solve(Pt pt) {
		DateTime st=DateTime.Now;
		var (n,m)=sc.Tp2<int>();
		h=new (int,int)[n];
		g=new (int,int)[m];
		var wf=new long[n][];
		var wfi=new int[n][];
		g[0]=(300,300);
		g[1]=(300,500);
		g[2]=(300,700);
		g[3]=(500,300);
		g[4]=(500,700);
		g[5]=(700,300);
		g[6]=(700,500);
		g[7]=(700,700);
		for(int i=0;i<n;i++){
			wf[i]=new long[n];
			wfi[i]=new int[n];
			for(int j=0;j<n;j++){
				if(i!=j){wf[i][j]=inf;}
				wfi[i][j]=-1;
			}
		}
		for(int i = 0;i < n;i++) {
			h[i]=sc.Tp2<int>();
			for(int j = i - 1;j >= 0;j--) {wf[i][j]=wf[j][i]=Dis(h[i],h[j])*25;}
		}
		for(int i=0;i<n;i++){
			for(int j=0;j<n;j++){
				for(int k=0;k<n;k++){
					if(wf[j][k]>wf[j][i]+wf[i][k]) {
						wf[j][k]=wf[j][i]+wf[i][k];
						wfi[j][k]=i;
					}
				}
			}
		}
		var tn=n;
		var t=Enumerable.Range(0,tn).ToArray();
		var r=new int[tn];
		int v1=0,v2=2;
		double l1=Fu(t[v1],t[v1+1]),l2,l3,l4;
		int k1=-1,k2=-1;
		while((DateTime.Now-st).TotalMilliseconds<600){
			if(v1==k1&&v2==k2){
				break;
			}
			l2=Fu(t[v2],t[(v2+1)%tn]);
			l3=Fu(t[v1],t[v2]);
			l4=Fu(t[(v1+1)%tn],t[(v2+1)%tn]);
			if(l1+l2>l3+l4){
				int q=(v1+1)%tn,mm=v2+tn;
				if((v1==tn-1)||v1<v2){mm=v2;}
				for(int i=q;i<=mm;i++){r[tn-1-i+q]=t[i%tn];}
				for(int i=(tn-v2+q-1)%tn;i<tn;i++){t[(i+v2+1)%tn]=r[i];}
				l1=Fu(t[v1],t[(v1+1)%tn]);
				k1=v1;k2=v2;
			}
			if((v2+2)%tn==v1){
				v1=(v1+1)%tn;
				v2=(v1+2)%tn;
				l1=Fu(t[v1],t[(v1+1)%tn]);
			}
			else{v2=(v2+1)%tn;}
		}
		long Fu(int i,int j){return wf[i][j];}
		var lin=new List<(int,int)>();
		var lis=new List<(int,int)>();
		for(int i = 0;i < n;i++) {
			if(t[i]==0) {
				for(int j = 0;j < n;j++) {
					Ff(t[(i+j)%n],t[(i+j+1)%n]);
					void Ff(int a,int b) {
						if(wfi[a][b]!=-1) {
							Ff(a,wfi[a][b]);
							Ff(wfi[a][b],b);
						}
						else {
							Fg(a);
						}
					}
				}
				Fg(0);
				void Fg(int c) {
					lin.Add((1,c));
				}
				break;
			}
		}
		lis=lin;
		long sp=Fp(lin);
		Random ra=new Random(1);
		const int ty=950,tl=1,tu=3000,o=1000000000;
		var dd=(DateTime.Now-st).TotalMilliseconds;
		for(int l = 0;dd<ty;l++) {
			var tp=ty-dd;
			var ti=(int)tp/2;
			int y=(ra.Next(ti)+1)*((ra.Next(2)<<1)-1);
			int x=(ra.Next(ti)+1)*((ra.Next(2)<<1)-1);
			g[l%8]=(g[l%8].y+y,g[l%8].x+x);
			var lik=new List<(int,int)>();
			lik.Add(lin[0]);
			for(int i = 1;i < lin.Count;i++) {
				var p=Dis(h[lin[i-1].Item2],h[lin[i].Item2])*25;
				int d1=-1,d2=-1;
				for(int j = 0;j < m;j++) {
					var u=Dis(h[lin[i-1].Item2],g[j])*5+Dis(g[j],h[lin[i].Item2])*5;
					if(p>u) {
						p=u;
						d1=j;
					}
				}
				for(int j = 0;j < m;j++) {
					for(int k = 0;k < m;k++) {
						if(j==k) {continue;}
						var u=Dis(h[lin[i-1].Item2],g[j])*5+Dis(g[j],g[k])+Dis(g[k],h[lin[i].Item2])*5;
						if(p>u) {
							p=u;
							d1=j;
							d2=k;
						}
					}
				}
				if(d1!=-1) {
					lik.Add((2,d1));
					if(d2!=-1) {lik.Add((2,d2));}
				}
				lik.Add(lin[i]);
			}
			var kp=Fp(lik);
			if(kp>sp) {
				sp=kp;
				lis=new List<(int,int)>(lik);
			}
			else {
				g[l%8]=(g[l%8].y-y,g[l%8].x-x);
			}
			dd=(DateTime.Now-st).TotalMilliseconds;
		}
		for(int i = 0;i < m;i++) {
			pt.Wl(g[i].y,g[i].x);
		}
		pt.Wl(lis.Count);
		for(int i = 0;i < lis.Count;i++) {
			pt.Wl(lis[i].Item1,lis[i].Item2+1);
		}
	}
	static long Dis((int,int) a,(int,int) b) {return (a.Item1-b.Item1)*(a.Item1-b.Item1)+(a.Item2-b.Item2)*(a.Item2-b.Item2);}
	static long Fp(List<(int,int)> li) {
		long p=0;
		for(int i = 1;i < li.Count;i++) {
			p+=Fd(li[i-1],li[i]);
		}
		return (long)Round(1e9/(1000+Sqrt(p)));
	}
	static long Fd((int,int) a,(int,int) b) {
		long p=0;
		if(a.Item1==1&&b.Item1==1) {p=Dis(h[b.Item2],h[a.Item2])*25;}
		else if(a.Item1==2&&b.Item1==2) {p=Dis(g[b.Item2],g[a.Item2]);}
		else if(b.Item1==2) {p=Dis(g[b.Item2],h[a.Item2])*5;}
		else if(a.Item1==2) {p=Dis(h[b.Item2],g[a.Item2])*5;}
		return p;
	}
}
public class Pt{
	private StringBuilder sb=new StringBuilder();
	public Pt(Action<Pt> f){f(this);}
	public void W(int s){sb.Append(s);}
	public void W(long s){sb.Append(s);}
	public void W(double s){sb.Append(s);}
	public void W(decimal s){sb.Append(s);}
	public void W(char s){sb.Append(s);}
	public void W(string s){sb.Append(s);}
	public void W(object s){sb.Append(s);}
	public void W(params object[] s){sb.Append(string.Join(" ",s));}
	public void Wl(int s){sb.Append(s).Append(Environment.NewLine);}
	public void Wl(long s){sb.Append(s).Append(Environment.NewLine);}
	public void Wl(double s){sb.Append(s).Append(Environment.NewLine);}
	public void Wl(decimal s){sb.Append(s).Append(Environment.NewLine);}
	public void Wl(char s){sb.Append(s).Append(Environment.NewLine);}
	public void Wl(string s){sb.Append(s).Append(Environment.NewLine);}
	public void Wl(object s){sb.Append(s).Append(Environment.NewLine);}
	public void Wl(int[] s){sb.Append(string.Join(" ",s)).Append(Environment.NewLine);}
	public void Wl(long[] s){sb.Append(string.Join(" ",s)).Append(Environment.NewLine);}
	public void Wl(double[] s){sb.Append(string.Join(" ",s)).Append(Environment.NewLine);}
	public void Wl(string[] s){sb.Append(string.Join(" ",s)).Append(Environment.NewLine);}
	public void Wl(params object[] s){sb.Append(string.Join(" ",s)).Append(Environment.NewLine);}
	public void Wl(){sb.Append(Environment.NewLine);}
	public void Sm(){Console.Write(sb);}
	public void Op(StreamWriter sw){
		sw.Write(sb);
		sw.Close();
	}
	public static bool operator==(Pt a,Pt b){return a.sb.ToString()==b.sb.ToString();}
	public static bool operator!=(Pt a,Pt b){return a.sb.ToString()!=b.sb.ToString();}
	public override bool Equals(object obj){return false;}
	public override int GetHashCode(){return 0;}
}
public class Sc{
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	protected virtual string Rl(){return Console.ReadLine();}
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	protected virtual string[] Sp(string st){return st.Split();}
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	private T Ct<T>(string s){return (T)Convert.ChangeType(s,typeof(T));}
	public virtual int I{get{return int.Parse(Rl());}}
	public virtual long L{get{return long.Parse(Rl());}}
	public virtual double D{get{return double.Parse(Rl());}}
	public virtual string S{get{return Rl();}}
	public int[] Ia{get{return Array.ConvertAll(Sp(Rl()),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Sp(Rl()),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Sp(Rl()),double.Parse);}}
	public string[] Sa{get{return Sp(Rl());}}
	public object[] Oa{get{return Sp(Rl());}}
	public int[] Ia2{get{return Array.ConvertAll(Sp("0 "+Rl()+" 0"),int.Parse);}}
	public int[] Ia3(string a,string b){return Array.ConvertAll(Sp(a+Rl()+b),int.Parse);}
	public int[] Ia3(int a){return Array.ConvertAll(Sp(Rl()+" "+a.ToString()),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(Sp("0 "+Rl()+" 0"),long.Parse);}}
	public long[] La3(string a,string b){return Array.ConvertAll(Sp(a+Rl()+b),long.Parse);}
	public long[] La3(int a){return Array.ConvertAll(Sp(Rl()+" "+a.ToString()),long.Parse);}
	public double[] Da2{get{return Array.ConvertAll(Sp("0 "+Rl()+" 0"),double.Parse);}}
	public double[] Da3(string a,string b){return Array.ConvertAll(Sp(a+Rl()+b),double.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Sp(Rl()));}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Sp(Rl()));}return a;}
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public (T,T) Tp2<T>(){var s=Sp(Rl());return (Ct<T>(s[0]),Ct<T>(s[1]));}
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public (T,T,T) Tp3<T>(){var s=Sp(Rl());return (Ct<T>(s[0]),Ct<T>(s[1]),Ct<T>(s[2]));}
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public (T,T,T,T) Tp4<T>(){var s=Sp(Rl());return (Ct<T>(s[0]),Ct<T>(s[1]),Ct<T>(s[2]),Ct<T>(s[3]));}
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public (T,T,T,T,T) Tp5<T>(){var s=Sp(Rl());return (Ct<T>(s[0]),Ct<T>(s[1]),Ct<T>(s[2]),Ct<T>(s[3]),Ct<T>(s[4]));}
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public (T,T,T,T,T,T) Tp6<T>(){var s=Sp(Rl());return (Ct<T>(s[0]),Ct<T>(s[1]),Ct<T>(s[2]),Ct<T>(s[3]),Ct<T>(s[4]),Ct<T>(s[5]));}
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public (T1,T2) Tp2<T1,T2>(){var s=Sp(Rl());return (Ct<T1>(s[0]),Ct<T2>(s[1]));}
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	public (T1,T1,T2) Tp3<T1,T2>(){var s=Sp(Rl());return (Ct<T1>(s[0]),Ct<T1>(s[1]),Ct<T2>(s[2]));}
}
public class Scr:Sc{
	private List<string> li=new List<string>();
	private int l=0;
	private bool bo=false;
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	protected override string Rl(){
		if(bo){return li[l++%li.Count];}
		li.Add(Console.ReadLine());
		return li[li.Count-1];
	}
	public void Again(){bo=true;}
}
public class Scs:Sc{
	private StreamReader sr;
	public Scs(string t){sr=new StreamReader(t);}
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	protected override string Rl(){return sr.ReadLine();}
	public void Close(){sr.Close();}
}
public class Sc2:Sc{
	private string[] sps=new string[]{" ","　","\t"};
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	protected override string[] Sp(string st){return st.Split(sps,StringSplitOptions.RemoveEmptyEntries);}
	public override int I{get{return int.Parse(Sp(Rl())[0]);}}
	public override long L{get{return long.Parse(Sp(Rl())[0]);}}
	public override double D{get{return double.Parse(Sp(Rl())[0]);}}
	public override string S{get{return Sp(Rl())[0];}}
}
public class Scs2:Sc2{
	private StreamReader sr;
	public Scs2(string t){sr=new StreamReader(t);}
	[MethodImpl(MethodImplOptions.AggressiveInlining)]
	protected override string Rl(){return sr.ReadLine();}
	public void Close(){sr.Close();}
}
public class Sct:Sc{
	private List<string> li=new List<string>();
	private int l=0;
	public void Add(int s){li.Add(s.ToString());}
	public void Add(long s){li.Add(s.ToString());}
	public void Add(double s){li.Add(s.ToString());}
	public void Add(string s){li.Add(s.ToString());}
	public void Add(object s){li.Add(s.ToString());}
	public void Add(int[] s){li.Add(string.Join(" ",s));}
	public void Add(long[] s){li.Add(string.Join(" ",s));}
	public void Add(double[] s){li.Add(string.Join(" ",s));}
	public void Add(string[] s){li.Add(string.Join(" ",s));}
	public void Add(object[] s){li.Add(string.Join(" ",s));}
	protected override string Rl(){return li[l++];}
	public void Clear(){li.Clear();l=0;}
	public void Again(){l=0;}
	public void Pf(){Console.WriteLine(string.Join("\n",li));}
}