Problem: There is a strange peculiarity: if you connect the cities of Rostov, Taganrog and Shakhty, peculiarly, you get a triangle

«Unbelievable But True»

Students from many different parts of Russia and abroad come to Summer Informatics School. You marked the hometowns of the SIS participants on a map.

Now you decided to prepare an interesting infographic based on this map. The first thing you chose to do is to find three cities on this map, such that they form a triangle with area S.

Input

The first line of input contains two integers n and S (3 ≤ n ≤ 2000, 1 ≤ S ≤ 2 ⋅ 10^{18}) — the number of cities on the map and the area of the triangle to be found.

The next n lines contain descriptions of the cities, one per line. Each city is described by its integer coordinates x_i, y_i (-10^9 ≤ x_i, y_i ≤ 10^9). 

It is guaranteed that all cities are located at distinct points. It is also guaranteed that no three cities lie on the same line.

Output

If the solution doesn't exist — print «No».

Otherwise, print «Yes», followed by three pairs of coordinates (x, y) — the locations of the three cities, which form the triangle of area S.

Examples

Input

3 7
0 0
3 0
0 4


Output

No


Input

4 3
0 0
2 0
1 2
1 3


Output

Yes
0 0
1 3
2 0

Solution (in JAVA):

Solution:
//package round503;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;

public class D3 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		long S = nl();
		int[][] co = new int[n][];
		for(int i = 0;i < n;i++){
			co[i] = new int[]{ni(), ni()};
		}
		Arrays.sort(co, new Comparator<int[]>() {
			public int compare(int[] a, int[] b) {
				if(a[1] != b[1])return a[1] - b[1];
				return (a[0] - b[0]);
			}
		});
//		tr(co);
		
		int[][] vs = new int[n*(n-1)/2][];
		int p = 0;
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				if(i == j)continue;
				if(co[j][1]-co[i][1] > 0 || co[j][1]-co[i][1] == 0 && co[j][0]-co[i][0] > 0){
					vs[p++] = new int[]{
							co[j][0] - co[i][0], co[j][1]-co[i][1], i, j
					};
				}
			}
		}
		mergesort(vs, 0, vs.length);
//		Arrays.sort(vs, compArgi);
//		
//		vs = Arrays.copyOf(vs, n*(n-1));
//		for(int i = 0;i < n*(n-1)/2;i++){
//			vs[i+n*(n-1)/2] = new int[]{-vs[i][0], -vs[i][1], vs[i][3], vs[i][2]};
//		}
		
		int[] ord = new int[n];
		for(int i = 0;i < n;i++){
			ord[i] = i;
		}
		int[] iord = new int[n];
		for(int i = 0;i < n;i++){
			iord[ord[i]] = i;
		}
		
		int u = vs.length*2;
		for(int ii = 0, i = 0;ii < u;ii++,i++){
			if(i == u/2)i -= u/2;
			if(ii >= u/2){
				vs[i][0] = -vs[i][0];
				vs[i][1] = -vs[i][1];
				int d = vs[i][2]; vs[i][2] = vs[i][3]; vs[i][3] = d;
			}
			
			int sa = vs[i][2];
			int sb = vs[i][3];
			int pa = iord[sa];
			int pb = iord[sb];
			ord[pa] = sb;
			ord[pb] = sa;
			iord[sa] = pb;
			iord[sb] = pa;
//			long[] lvs = new long[n];
//			for(int o = 0;o < n;o++){
//				long val = 
//						(long)(co[ord[o]][0]-co[sa][0])*(co[sb][1]-co[sa][1]) - 
//						(long)(co[ord[o]][1]-co[sa][1])*(co[sb][0]-co[sa][0]);
//				lvs[o] = val;
//			}
//			tr();
//			tr(lvs);
			
			// x1y2-y1x2 = 2S or -2S
			{
				long v0 = f(0, co, sa, sb);
				long vj = f(n-1, co, sa, sb);
				if(v0 < vj){
//					{
//						int low = 0, high = n;
//						while(high - low > 1){
//							int h = high+low>>1;
//							
//							long val = f(ord[h], co, sa, sb);
//							if(val <= 2*S){
//								low = h;
//							}else{
//								high = h;
//							}
//						}
//						long val = f(ord[low], co, sa, sb);
//						if(val == 2*S){
//							out.println("Yes");
//							out.println(co[sa][0] + " " + co[sa][1]);
//							out.println(co[sb][0] + " " + co[sb][1]);
//							out.println(co[ord[low]][0] + " " + co[ord[low]][1]);
//							return;
//						}
//					}
				}else{
					{
						int low = 0, high = n;
						while(high - low > 1){
							int h = high+low>>1;
							
							long val = f(ord[h], co, sa, sb);
							if(val >= 2*S){
								low = h;
							}else{
								high = h;
							}
						}
						long val = f(ord[low], co, sa, sb);
						if(val == 2*S){
							out.println("Yes");
							out.println(co[sa][0] + " " + co[sa][1]);
							out.println(co[sb][0] + " " + co[sb][1]);
							out.println(co[ord[low]][0] + " " + co[ord[low]][1]);
							return;
						}
					}
				}
			}
//			tr(ord);
		}
		out.println("No");
	}
	
	private static int[][] stemp = new int[2000000][];
	
	public static void mergesort(int[][] a, int s, int e)
	{
		if(e - s <= 1)return;
		int h = s+e>>1;
		mergesort(a, s, h);
		mergesort(a, h, e);
		int p = 0;
		int i= s, j = h;
		for(;i < h && j < e;)stemp[p++] = compare(a[i], a[j]) ? a[i++] : a[j++];
		while(i < h)stemp[p++] = a[i++];
		while(j < e)stemp[p++] = a[j++];
		System.arraycopy(stemp, 0, a, s, e-s);
	}

	
	long f(int x, int[][] co, int sa, int sb)
	{
		return
				(long)(co[x][0]-co[sa][0])*(co[sb][1]-co[sa][1]) - 
				(long)(co[x][1]-co[sa][1])*(co[sb][0]-co[sa][0]);
	}
	
	public static boolean compare(int[] a, int[] b)
	{
		long ax = a[0], ay = a[1];
		long bx = b[0], by = b[1];
		int za = ay > 0 || ay == 0 && ax > 0 ? 0 : 1;
		int zb = by > 0 || by == 0 && bx > 0 ? 0 : 1;
		if(za != zb)return za < zb;
		if(ay*bx-ax*by != 0)return ay*bx-ax*by < 0;
		return (ax*ax+ay*ay)-(bx*bx+by*by) < 0;
	}
	
//	public static Comparator<int[]> compArgi = new Comparator<int[]>(){
//		public int compare(int[] a, int[] b)
//		{
//			long ax = a[0], ay = a[1];
//			long bx = b[0], by = b[1];
//			int za = ay > 0 || ay == 0 && ax > 0 ? 0 : 1;
//			int zb = by > 0 || by == 0 && bx > 0 ? 0 : 1;
//			if(za != zb)return za - zb;
//			if(ay*bx-ax*by != 0)return Long.signum(ay*bx-ax*by);
//			return Long.signum((ax*ax+ay*ay)-(bx*bx+by*by));
//		}
//	};

	
	void run() throws Exception
	{
//		int n = 2000, m = 99999;
//		Random gen = new Random();
//		StringBuilder sb = new StringBuilder();
//		sb.append(n + " ");
//		sb.append(m + " ");
//		for (int i = 0; i < n; i++) {
//			sb.append(gen.nextInt(2000000000)-1000000000 + " ");
//			sb.append(gen.nextInt(2000000000)-1000000000 + " ");
//		}
//		INPUT = sb.toString();

		
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new D3().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}