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:
/*
Keep solving problems.
*/

import java.util.*;
import java.io.*;

public class CFA {
    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;
    private static final long MOD = 1000 * 1000 * 1000 + 7;
    private static final int[] dx = {0, -1, 0, 1};
    private static final int[] dy = {1, 0, -1, 0};
    private static final String yes = "Yes";
    private static final String no = "No";

    class Pair implements Comparable<Pair> {
        long amount;
        long temp;
        public Pair(long amount, long temp) {
            this.amount = amount;
            this.temp = temp;
        }

        @Override
        public int compareTo(Pair o) {
            return Long.compare(this.temp, o.temp);
        }
    }
    void solve() throws IOException {
        int n = nextInt();
        int T = nextInt();
        long[] a = nextLongArr(n);
        long[] t = nextLongArr(n);
        Pair[] arr = new Pair[n];
        for (int i = 0; i < n; i++) {
            arr[i] = new Pair(a[i], t[i] - T);
        }
        long sum = 0;
        for (int i = 0; i < n; i++) {
            sum += a[i] * (t[i] - T);
        }
        if (sum == 0) {
            long res = 0;
            for (long v : a) {
                res += v;
            }
            outln(res);
            return;
        }
        Arrays.sort(arr);
        double res = 0;
        if (sum > 0) {
            long need = 0;
            int i = 0;
            while (i < n) {
                Pair cur = arr[i];
                if (cur.temp <= 0) {
                    res += cur.amount;
                    need += (-cur.temp) * cur.amount;
                }
                else {
                    break;
                }
                i++;
            }

            while (i < n) {
                Pair cur = arr[i];
                long has = cur.temp * cur.amount;
                if (need <= has) {
                    res += 1.0 * need / cur.temp;
                    need = 0;
                }
                else {
                    need -= has;
                    res += cur.amount;
                }

                if (need == 0) {
                    break;
                }
                i++;
            }
        }
        else {
            long need = 0;
            int i = n - 1;
            while (i >= 0) {
                Pair cur = arr[i];
                if (cur.temp >= 0) {
                    res += cur.amount;
                    need += cur.temp * cur.amount;
                }
                else {
                    break;
                }
                i--;
            }

            while (i >= 0) {
                Pair cur = arr[i];
                long has = (-cur.temp) * cur.amount;
                if (need <= has) {
                    res += 1.0 * need / (-cur.temp);
                    need = 0;
                } else {
                    need -= has;
                    res += cur.amount;
                }

                if (need == 0) {
                    break;
                }
                i--;
            }
        }

        formatPrint(res);
    }

    void shuffle(int[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            int tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }

    long gcd(long a, long b) {
        while(a != 0 && b != 0) {
            long c = b;
            b = a % b;
            a = c;
        }
        return a + b;
    }

    private void outln(Object o) {
        out.println(o);
    }
    private void out(Object o) {
        out.print(o);
    }
    private void formatPrint(double val) {
        System.out.format("%.9f%n", val);
    }
    public CFA() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CFA();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}