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:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Div1_503D {

	public static void main(String[] args) throws IOException {
		new Div1_503D().execute();
	}

	int N;
	Pt[] pts;

	void execute() throws IOException {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter printer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		StringTokenizer inputData = new StringTokenizer(reader.readLine());
		N = Integer.parseInt(inputData.nextToken());
		long tar = Long.parseLong(inputData.nextToken()) * 2;

		pts = new Pt[N];

		for (int i = 0; i < N; i++) {
			inputData = new StringTokenizer(reader.readLine());
			pts[i] = new Pt(Integer.parseInt(inputData.nextToken()), Integer.parseInt(inputData.nextToken()), i);
		}

		Arrays.sort(pts);

		int[] pos = new int[N];
		for (int i = 0; i < N; i++) {
			pos[pts[i].i] = i;
		}

		Line[] lines = new Line[N * (N - 1) / 2];

		int nLine = 0;
		for (int i = 0; i < N; i++) {
			for (int j = i + 1; j < N; j++) {
				lines[nLine++] = new Line(pts[i], pts[j]);
			}
		}
		Arrays.sort(lines);

		for (Line cLine : lines) {
			Pt ptA = cLine.a;
			Pt ptB = cLine.b;

			int posA = pos[ptA.i];
			int posB = pos[ptB.i];

			pts[posA] = ptB;
			pts[posB] = ptA;

			pos[ptA.i] = posB;
			pos[ptB.i] = posA;

			Pt ret = search(cLine, tar);
			if (ret != null) {
				printer.println("Yes");
				printer.println(cLine.a.x + " " + cLine.a.y);
				printer.println(cLine.b.x + " " + cLine.b.y);
				printer.println(ret.x + " " + ret.y);
				printer.close();
				return;
			}

			ret = search(cLine, -tar);
			if (ret != null) {
				printer.println("Yes");
				printer.println(cLine.a.x + " " + cLine.a.y);
				printer.println(cLine.b.x + " " + cLine.b.y);
				printer.println(ret.x + " " + ret.y);
				printer.close();
				return;
			}
		}
		printer.println("No");
		printer.close();
	}

	Pt search(Line base, long tar) {
		int low = 0;
		int high = N - 1;
		while (low <= high) {
			int mid = (low + high) >> 1;
			long cArea = tArea(base, pts[mid]);
			if (cArea == tar) {
				return pts[mid];
			} else if (cArea < tar) {
				low = mid + 1;
			} else {
				high = mid - 1;
			}
		}
		return null;
	}

	long tArea(Line base, Pt ext) {
		int v1x = base.b.x - base.a.x;
		int v1y = base.b.y - base.a.y;
		int v2x = ext.x - base.a.x;
		int v2y = ext.y - base.a.y;

		return (long) v1x * v2y - (long) v1y * v2x;
	}

	class Pt implements Comparable<Pt> {
		int x;
		int y;
		int i;

		Pt(int x, int y, int i) {
			this.x = x;
			this.y = y;
			this.i = i;
		}

		public int compareTo(Pt o) {
			if (y != o.y) {
				return Integer.compare(y, o.y);
			} else {
				return Integer.compare(x, o.x);
			}
		}
	}

	class Line implements Comparable<Line> {
		Pt a;
		Pt b;
		double angle;

		Line(Pt a, Pt b) {
			this.a = a;
			this.b = b;

			if (a.y > b.y || (a.y == b.y && a.x > b.x)) {
				Pt t = a;
				a = b;
				b = t;
			}

			angle = Math.atan2(b.y - a.y, b.x - a.x);
		}

		public int compareTo(Line o) {
			return Double.compare(angle, o.angle);
		}
	}
}