Problem: Gosha is hunting. His goal is to catch as many Pokemons as possible. Gosha has a Poke Balls and b Ultra Balls. There are n Pokemons. They are numbered 1 through n. Gosha knows that if he throws a Poke Ball at the i-th Pokemon he catches it with probability pi. If he throws an Ultra Ball at the i-th Pokemon he catches it with probability ui. He can throw at most one Ball of each type at any Pokemon.

The hunting proceeds as follows: at first, Gosha chooses no more than a Pokemons at which he will throw Poke Balls and no more than b Pokemons at which he will throw Ultra Balls. After that, he throws the chosen Balls at the chosen Pokemons. If he throws both Ultra Ball and Poke Ball at some Pokemon, he is caught if and only if he is caught by any of these Balls. The outcome of a throw doesn't depend on the other throws.

Gosha would like to know what is the expected number of the Pokemons he catches if he acts in an optimal way. In other words, he would like to know the maximum possible expected number of Pokemons can catch.

Input

The first line contains three integers n, a and b (2 ≤ n ≤ 2000, 0 ≤ a, b ≤ n) — the number of Pokemons, the number of Poke Balls and the number of Ultra Balls.

The second line contains n real values p1, p2, ..., pn (0 ≤ pi ≤ 1), where pi is the probability of catching the i-th Pokemon if Gosha throws a Poke Ball to it.

The third line contains n real values u1, u2, ..., un (0 ≤ ui ≤ 1), where ui is the probability of catching the i-th Pokemon if Gosha throws an Ultra Ball to it.

All the probabilities are given with exactly three digits after the decimal separator.

Output

Print the maximum possible expected number of Pokemons Gosha can catch. The answer is considered correct if it's absolute or relative error doesn't exceed 10 - 4.

Examples

Input

3 2 2
1.000 0.000 0.500
0.000 1.000 0.500


Output

2.75


Input

4 1 3
0.100 0.500 0.500 0.600
0.100 0.500 0.900 0.400


Output

2.16


Input

3 2 0
0.412 0.198 0.599
0.612 0.987 0.443


Output

1.011

Solution (in JAVA):

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

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

    static class EGoshaIsHunting {
        void resolve(double[] dp, int[] cnta, int[] cntb, int ind, double newVal, int newCnta, int newCntb) {
            if (newVal > dp[ind]) {
                dp[ind] = newVal;
                cnta[ind] = newCnta;
                cntb[ind] = newCntb;
            } else if (newVal == dp[ind] && cnta[ind] > newCnta) {
                cntb[ind] = newCntb;
                cnta[ind] = newCnta;
            } else if (newVal == dp[ind] && cnta[ind] == newCnta && cntb[ind] > newCntb)
                cntb[ind] = newCntb;
        }

        public void solve(int testNumber, InputReader sc, PrintWriter out) {
            int n = sc.nextInt();
            int a = sc.nextInt();
            int b = sc.nextInt();

            double p[] = new double[n + 1];
            for (int i = 1; i <= n; ++i)
                p[i] = sc.nextDouble();

            double u[] = new double[n + 1];
            for (int i = 1; i <= n; ++i)
                u[i] = sc.nextDouble();

            double starta = 0.0, enda = 10.0;
            double ans = 0.0;
            for (int i = 0; i < 100; ++i) {
                double mida = (starta + enda) * 0.5;

                double startb = 0.0, endb = 1.0;
                double cans = 0.0;
                int canscnta = -1;
                for (int j = 0; j < 100; ++j) {
                    double midb = (startb + endb) * 0.5;

                    double dp[] = new double[n + 1];
                    int cntb[] = new int[n + 1];
                    int cnta[] = new int[n + 1];

                    for (int k = 1; k <= n; ++k) {
                        dp[k] = dp[k - 1];
                        cntb[k] = cntb[k - 1];
                        cnta[k] = cnta[k - 1];

                        resolve(dp, cnta, cntb, k, dp[k - 1] + p[k] - mida, cnta[k - 1] + 1, cntb[k - 1]);
                        resolve(dp, cnta, cntb, k, dp[k - 1] + u[k] - midb, cnta[k - 1], cntb[k - 1] + 1);
                        resolve(dp, cnta, cntb, k, dp[k - 1] + u[k] + p[k] - u[k] * p[k] - mida - midb, cnta[k - 1] + 1, cntb[k - 1] + 1);
                    }

                    if (cntb[n] > b) {
                        startb = midb;
                    } else {
                        endb = midb;
                        cans = dp[n] + midb * b;
                        canscnta = cnta[n];
                    }
                }

                if (canscnta > a) {
                    starta = mida;
                } else {
                    ans = cans + mida * a;
                    enda = mida;
                }
            }

            out.print(ans);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public 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++];
        }

        public int nextInt() {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}