Problem: Consider a system of n water taps all pouring water into the same container. The i-th water tap can be set to deliver any amount of water from 0 to ai ml per second (this amount may be a real number). The water delivered by i-th tap has temperature ti.

If for every <image> you set i-th tap to deliver exactly xi ml of water per second, then the resulting temperature of water will be <image> (if <image>, then to avoid division by zero we state that the resulting water temperature is 0).

You have to set all the water taps in such a way that the resulting temperature is exactly T. What is the maximum amount of water you may get per second if its temperature has to be T?

Input

The first line contains two integers n and T (1 ≤ n ≤ 200000, 1 ≤ T ≤ 106) — the number of water taps and the desired temperature of water, respectively.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106) where ai is the maximum amount of water i-th tap can deliver per second.

The third line contains n integers t1, t2, ..., tn (1 ≤ ti ≤ 106) — the temperature of water each tap delivers.

Output

Print the maximum possible amount of water with temperature exactly T you can get per second (if it is impossible to obtain water with such temperature, then the answer is considered to be 0).

Your answer is considered correct if its absolute or relative error doesn't exceed 10 - 6.

Examples

Input

2 100
3 10
50 150


Output

6.000000000000000


Input

3 9
5 5 30
6 6 10


Output

40.000000000000000


Input

2 12
1 3
10 15


Output

1.666666666666667

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInputReader in = new MyInputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        long[] sumTemp;
        long[] sumX;

        long sumTemp(int from, int to) {
            if (from > 0) {
                return sumTemp[to] - sumTemp[from - 1];
            }
            return sumTemp[to];
        }

        long sumX(int from, int to) {
            if (from > 0) {
                return sumX[to] - sumX[from - 1];
            }
            return sumX[to];
        }

        public void solve(int testNumber, MyInputReader in, PrintWriter out) {
            int n = in.nextInt();
            long T = in.nextInt();
            int[] a = new int[n];
            int[] t = new int[n];
            Pair[] pairs = new Pair[n];

            sumTemp = new long[n];
            sumX = new long[n];

            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
            }
            for (int i = 0; i < n; i++) {
                t[i] = in.nextInt();
            }

            for (int i = 0; i < n; i++) {
                pairs[i] = new Pair(t[i], a[i]);
            }
            t = null;
            a = null;
            Arrays.sort(pairs);

            for (int i = 0; i < n; i++) {
                sumTemp[i] = (long) pairs[i].temperature * pairs[i].maxWater;
                if (i > 0) sumTemp[i] += sumTemp[i - 1];

                sumX[i] = (long) pairs[i].maxWater;
                if (i > 0) sumX[i] += sumX[i - 1];
            }


            if (sumTemp[n - 1] == T * sumX[n - 1]) {
                double ans = sumX[n - 1];
                out.println(ans);
                return;
            }

            long test = sumTemp(0, n - 1);
            long test2 = T * sumX[n - 1];
            double EPS = 1e-9;
            if (test > test2) {
                int i = n - 1;

                while (i >= 0 && sumTemp(0, i) > T * sumX(0, i)) {
                    i--;
                }

                if (i == -1) {
                    out.println(0);
                    return;
                }
                double lo = 0;
                double hi = pairs[i + 1].maxWater;

                long aa = sumTemp(0, i);
                long bb = sumX(0, i);
                while (lo + EPS < hi) {
                    double mid = (hi + lo) / 2;
                    if (aa + (mid * pairs[i + 1].temperature) < T * (bb + mid)) {
                        lo = mid;
                    } else {
                        hi = mid;
                    }
                }
                out.printf("%.20f\n", bb + lo);
            } else {
                int i = 0;

                while (i < n && sumTemp(i, n - 1) < T * sumX(i, n - 1)) {
                    i++;
                }
                if (i == n) {
                    out.println(0);
                    return;
                }

                double lo = 0;
                double hi = pairs[i - 1].maxWater;

                long aa = sumTemp(i, n - 1);
                long bb = sumX(i, n - 1);
                while (lo + EPS < hi) {
                    double mid = (hi + lo) / 2;
                    if (aa + (mid * pairs[i - 1].temperature) > T * (bb + mid)) {
                        lo = mid;
                    } else {
                        hi = mid;
                    }
                }
                out.printf("%.20f\n", bb + lo);
            }
        }

        class Pair implements Comparable<Pair> {
            int temperature;
            int maxWater;

            public Pair(int temperature, int maxWater) {
                this.temperature = temperature;
                this.maxWater = maxWater;
            }


            public int compareTo(Pair o) {
                if (this.temperature == o.temperature) return o.maxWater - this.maxWater;
                return this.temperature - o.temperature;
            }

        }

    }

    static class MyInputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public MyInputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    String l = reader.readLine();
                    if (l == null) {
                        return null;
                    }
                    tokenizer = new StringTokenizer(l);
                } catch (Exception e) {
                    //return null;
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}