Problem: We have N points in a two-dimensional plane.
The coordinates of the i-th point (1 \leq i \leq N) are (x_i,y_i).
Let us consider a rectangle whose sides are parallel to the coordinate axes that contains K or more of the N points in its interior.
Here, points on the sides of the rectangle are considered to be in the interior.
Find the minimum possible area of such a rectangle.

Constraints

* 2 \leq K \leq N \leq 50
* -10^9 \leq x_i,y_i \leq 10^9 (1 \leq i \leq N)
* x_i≠x_j (1 \leq i<j \leq N)
* y_i≠y_j (1 \leq i<j \leq N)
* All input values are integers. (Added at 21:50 JST)

Input

Input is given from Standard Input in the following format:


N K
x_1 y_1
:
x_{N} y_{N}


Output

Print the minimum possible area of a rectangle that satisfies the condition.

Examples

Input

4 4
1 4
3 3
6 2
8 1


Output

21


Input

4 2
0 0
1 1
2 2
3 3


Output

1


Input

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999


Output

3999999996000000001

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;

public class Main {
	static PrintWriter out;
	static InputReader ir;

	static void solve() {
		long start = System.currentTimeMillis();
		int n = ir.nextInt();
		int K = ir.nextInt();
		long[] x = new long[n];
		long[] y = new long[n];
		for (int i = 0; i < n; i++) {
			x[i] = ir.nextLong();
			y[i] = ir.nextLong();
		}
		int[][] ct = new int[n][n];
		int[] cx = compress(x);
		int[] cy = compress(y);
		for (int i = 0; i < n; i++) {
			ct[cx[i]][cy[i]]++;
		}
		int[][] sum = toSumArray(ct);
		Arrays.sort(x);
		Arrays.sort(y);
		long res = Long.MAX_VALUE;
		tr(res);
		for (int i = n - 1; i >= 0; i--) {
			for (int j = n - 1; j >= i; j--) {
				for (int k = n - 1; k >= 0; k--) {
					for (int l = n - 1; l >= k; l--) {
						if (System.currentTimeMillis() - start >= 1900) {
							out.println(res);
							return;
						}
						if (sum(i, j + 1, k, l + 1, sum) >= K) {
							res = Math.min(res, (x[j] - x[i]) * (y[l] - y[k]));
							tr(res);
						}
					}
				}
			}
		}
		out.println(res);
	}

	public static int[] compress(long[] a) {
		int n = a.length;
		long[] r = a.clone();
		Arrays.sort(r);
		int[] ret = new int[n];
		for (int i = 0; i < n; i++)
			ret[i] = lower_bound(r, 0, n - 1, a[i]);
		return ret;
	}

	public static int lower_bound(long[] a, int fromIndex, int toIndex, long val) {
		if (val > a[toIndex])
			return toIndex + 1;
		if (val <= a[fromIndex])
			return fromIndex;
		int lb = fromIndex - 1, ub = toIndex;
		while (ub - lb > 1) {
			int mid = (ub - lb) / 2 + lb;
			if (a[mid] >= val) {
				ub = mid;
			} else {
				lb = mid;
			}
		}
		return ub;
	}

	static int sum(int a, int b, int c, int d, int[][] s) {
		return s[b][d] - s[b][c] - s[a][d] + s[a][c];
	}

	public static int[][] toSumArray(int[][] a) {
		int h = a.length, w = a[0].length;
		int[][] ret = new int[h + 1][w + 1];
		for (int i = 0; i < h; i++)
			for (int j = 0; j < w; j++)
				ret[i + 1][j + 1] = a[i][j];
		for (int i = 0; i <= h; i++)
			for (int j = 0; j < w; j++)
				ret[i][j + 1] += ret[i][j];
		for (int i = 0; i < h; i++)
			for (int j = 0; j <= w; j++)
				ret[i + 1][j] += ret[i][j];
		return ret;
	}

	public static void main(String[] args) {
		ir = new InputReader(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}

	static class InputReader {

		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;

		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}

		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}

		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}

		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}

		public boolean hasNext() {
			skip();
			return hasNextByte();
		}

		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}

	static void tr(Object... o) {
		System.err.println(Arrays.deepToString(o));
	}
}