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.*;
import java.util.Arrays;
import java.util.Comparator;

/**
 * Created by dalt on 2018/4/2.
 */
public class CF954E {
    public static BlockReader input;
    public static PrintStream output;

    public static void main(String[] args) throws FileNotFoundException {
        if (System.getProperty("ONLINE_JUDGE") == null) {
            input = new BlockReader(new FileInputStream("D:\\DataBase\\TESTCASE\\codeforces\\CF954E.in"));
            output = System.out;
        } else {
            input = new BlockReader(System.in);
            output = new PrintStream(new BufferedOutputStream(System.out), false);
        }

        solve();

        output.flush();
    }

    public static void solve() {
        int n = input.nextInteger();
        int T = input.nextInteger();
        int[] cap = new int[n + 1];
        int[] temperature = new int[n + 1];
        int[][] neg = new int[n][2];
        int negLen = 0;
        int[][] pos = new int[n][2];
        int posLen = 0;
        double negSum = 0;
        double posSum = 0;
        for (int i = 1; i <= n; i++) {
            cap[i] = input.nextInteger();
        }

        double fix = 0;
        for (int j = 1; j <= n; j++) {
            temperature[j] = input.nextInteger() - T;
            if (temperature[j] > 0) {
                pos[posLen][0] = cap[j];
                pos[posLen][1] = temperature[j];
                posSum += (double) pos[posLen][0] * pos[posLen][1];
                posLen++;
            } else if (temperature[j] < 0) {
                neg[negLen][0] = cap[j];
                neg[negLen][1] = -temperature[j];
                negSum += (double) neg[negLen][0] * neg[negLen][1];
                negLen++;
            } else {
                fix += cap[j];
            }
        }

        Comparator<int[]> comparator = new Comparator<int[]>() {
            @Override
            public int compare(int[] o1, int[] o2) {
                return o1[1] - o2[1];
            }
        };
        Arrays.sort(pos, 0, posLen, comparator);
        Arrays.sort(neg, 0, negLen, comparator);

        double min = Math.min(posSum, negSum);
        double result = maxFlow(pos, posLen, min) + maxFlow(neg, negLen, min) + fix;

        output.println(String.format("%.13f", result));
    }

    public static double maxFlow(int[][] data, int len, double sum) {
        double total = 0;
        for (int i = 0; i < len && sum > 0; i++) {
            double occupied = Math.min(sum / data[i][1], data[i][0]);
            sum -= occupied * data[i][1];
            total += occupied;
        }
        return total;
    }

    public static class BlockReader {
        static final int EOF = -1;
        InputStream is;
        byte[] dBuf;
        int dPos, dSize, next;
        StringBuilder builder = new StringBuilder();

        public BlockReader(InputStream is) {
            this(is, 4096);
        }

        public BlockReader(InputStream is, int bufSize) {
            this.is = is;
            dBuf = new byte[bufSize];
            next = nextByte();
        }

        public int nextByte() {
            while (dPos >= dSize) {
                if (dSize == -1) {
                    return EOF;
                }
                dPos = 0;
                try {
                    dSize = is.read(dBuf);
                } catch (Exception e) {
                }
            }
            return dBuf[dPos++];
        }

        public String nextBlock() {
            builder.setLength(0);
            skipBlank();
            while (next != EOF && !Character.isWhitespace(next)) {
                builder.append((char) next);
                next = nextByte();
            }
            return builder.toString();
        }

        public void skipBlank() {
            while (Character.isWhitespace(next)) {
                next = nextByte();
            }
        }

        public int nextInteger() {
            skipBlank();
            int ret = 0;
            boolean rev = false;
            if (next == '+' || next == '-') {
                rev = next == '-';
                next = nextByte();
            }
            while (next >= '0' && next <= '9') {
                ret = (ret << 3) + (ret << 1) + next - '0';
                next = nextByte();
            }
            return rev ? -ret : ret;
        }

        public int nextBlock(char[] data, int offset) {
            skipBlank();
            int index = offset;
            int bound = data.length;
            while (next != EOF && index < bound && !Character.isWhitespace(next)) {
                data[index++] = (char) next;
                next = nextByte();
            }
            return index - offset;
        }

        public boolean hasMore() {
            skipBlank();
            return next != EOF;
        }
    }
}