Problem: A country Gizevom is being under a sneak and fierce attack by their foe. They have to deploy one or more troops to every base immediately in order to defend their country. Otherwise their foe would take all the bases and declare "All your base are belong to us."

You are asked to write a program that calculates the minimum time required for deployment, given the present positions and marching speeds of troops and the positions of the bases.



Input

The input consists of multiple datasets. Each dataset has the following format:

N M
x1 y1 v1
x2 y2 v2
...
xN yN vN
x'1 y'1
x'2 y'2
...
x'M y'M


N is the number of troops (1 ≤ N ≤ 100); M is the number of bases (1 ≤ M ≤ 100); (xi, yi ) denotes the present position of i-th troop; vi is the speed of the i-th troop (1 ≤ vi ≤ 100); (x'j, y'j) is the position of the j-th base.

All the coordinates are integers between 0 and 10000 inclusive.

The last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.

Output

For each dataset, print the minimum required time in a line.

Example

Input

2 2
10 20 1
0 10 1
0 10
10 0
0 0


Output

14.14213562

Solution (in JAVA):

Solution:

import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
	InputStream is;

	boolean __FILE_DEBUG_FLAG__ = false;
	String __DEBUG_FILE_NAME__ = "src/T";

	FastScanner in;
	PrintWriter out;
	
	/* ----------Bipartile Matching--------- */
	class BipartileMatching {
		int V;
		boolean[] used;
		int[] match;
		ArrayList<Integer>[] g;
		
		BipartileMatching(ArrayList<Integer>[] g) {
			V = g.length;
			used = new boolean[V];
			match = new int[V];
			this.g = g;
		}
		
		boolean dfs(int u) {
			used[u] = true;
			for (int v : g[u]) {
				int w = match[v];
				if (w < 0 || (!used[w] && dfs(w))) {
					match[v] = u;
					match[u] = v;
					return true;
				}
			}
			return false;
		}
		
		int doit() {
			int res = 0;
			Arrays.fill(match, -1);
			for (int v = 0; v < V; v++) {
				if (match[v] < 0) {
					Arrays.fill(used, false);
					if (dfs(v)) res++;
				}
			}
			return res;
		}
	}	
	/* ----------------------------- */
	
	double calcDist(double x1, double y1, double x2, double y2) {
		double dx = x1 - x2;
		double dy = y1 - y2;
		return Math.sqrt(dx * dx + dy * dy);
	}
	
	public void solve() {	
		while (true) {
			int n = in.nextInt(), m = in.nextInt();
			if (n == 0) break;
			
			int[] x = new int[n];
			int[] y = new int[n];
			int[] v = new int[n];
			for (int i = 0; i < n; i++) {
				x[i] = in.nextInt();
				y[i] = in.nextInt();
				v[i] = in.nextInt();
			}
			
			int[] mx = new int[m];
			int[] my = new int[m];
			for (int i = 0; i < m; i++) {
				mx[i] = in.nextInt();
				my[i] = in.nextInt();
			}
			
			double[][] baseGraph = new double[n][m];
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					double time = calcDist(x[i], y[i], mx[j], my[j]) / v[i];
					baseGraph[i][j] = time;
				}
			}
			
			@SuppressWarnings("unchecked")
			ArrayList<Integer>[] g = new ArrayList[n+m];
			for (int i = 0; i < n + m; i++) {
				g[i] = new ArrayList<Integer>();
			}
			double lo = 0, hi = 1e9;
			for (int times = 0; times < 120; times++) {
				double mid = (lo + hi) / 2;
				for (int i = 0; i < n + m; i++) {
					g[i].clear();
				}
				for (int i = 0; i < n; i++) {
					for (int j = 0; j < m; j++) {
						if (baseGraph[i][j] <= mid) {
							g[i].add(j+n);
							g[j+n].add(i);
						}
					}
				}
				BipartileMatching bm = new BipartileMatching(g);
				if (bm.doit() == m) 
					hi = mid;
				else
					lo = mid;
			}
			
			System.out.println(lo);
		}
	}

	
	public void run() {
		if (__FILE_DEBUG_FLAG__) {
			try {
				is = new FileInputStream(__DEBUG_FILE_NAME__);
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
			System.out.println("FILE_INPUT!!");
		} else {
			is = System.in;
		}
		in = new FastScanner(is);
		out = new PrintWriter(System.out);

		solve();
	}

	public static void main(String[] args) {
		new Main().run();
	}

	public void mapDebug(int[][] a) {
		System.out.println("--------map display---------");

		for (int i = 0; i < a.length; i++) {
			for (int j = 0; j < a[i].length; j++) {
				System.out.printf("%3d ", a[i][j]);
			}
			System.out.println();
		}

		System.out.println("----------------------------");
		System.out.println();
	}

	public void debug(Object... obj) {
		System.out.println(Arrays.deepToString(obj));
	}

	class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FastScanner(InputStream stream) {
			this.stream = stream;
			//stream = new FileInputStream(new File("dec.in"));

		}

		int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		int[] nextIntArray(int n) {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();

			return array;
		}

		int[][] nextIntMap(int n, int m) {
			int[][] map = new int[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextIntArray(m);
			}
			return map;
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		long[] nextLongArray(int n) {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();

			return array;
		}

		long[][] nextLongMap(int n, int m) {
			long[][] map = new long[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextLongArray(m);
			}
			return map;
		}

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

		double[] nextDoubleArray(int n) {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();

			return array;
		}

		double[][] nextDoubleMap(int n, int m) {
			double[][] map = new double[n][m];
			for (int i = 0; i < n; i++) {
				map[i] = in.nextDoubleArray(m);
			}
			return map;
		}

		String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		String[] nextStringArray(int n) {
			String[] array = new String[n];
			for (int i = 0; i < n; i++)
				array[i] = next();

			return array;
		}

		String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
}