Problem: One must train much to do well on wizardry contests. So, there are numerous wizardry schools and magic fees.

One of such magic schools consists of n tours. A winner of each tour gets a huge prize. The school is organised quite far away, so one will have to take all the prizes home in one go. And the bags that you've brought with you have space for no more than k huge prizes.

Besides the fact that you want to take all the prizes home, you also want to perform well. You will consider your performance good if you win at least l tours.

In fact, years of organizing contests proved to the organizers that transporting huge prizes is an issue for the participants. Alas, no one has ever invented a spell that would shrink the prizes... So, here's the solution: for some tours the winner gets a bag instead of a huge prize. Each bag is characterized by number ai — the number of huge prizes that will fit into it.

You already know the subject of all tours, so you can estimate the probability pi of winning the i-th tour. You cannot skip the tour under any circumstances.

Find the probability that you will perform well on the contest and will be able to take all won prizes home (that is, that you will be able to fit all the huge prizes that you won into the bags that you either won or brought from home).

Input

The first line contains three integers n, l, k (1 ≤ n ≤ 200, 0 ≤ l, k ≤ 200) — the number of tours, the minimum number of tours to win, and the number of prizes that you can fit in the bags brought from home, correspondingly.

The second line contains n space-separated integers, pi (0 ≤ pi ≤ 100) — the probability to win the i-th tour, in percents.

The third line contains n space-separated integers, ai (1 ≤ ai ≤ 200) — the capacity of the bag that will be awarded to you for winning the i-th tour, or else -1, if the prize for the i-th tour is a huge prize and not a bag.

Output

Print a single real number — the answer to the problem. The answer will be accepted if the absolute or relative error does not exceed 10 - 6.

Examples

Input

3 1 0
10 20 30
-1 -1 2


Output

0.300000000000


Input

1 1 1
100
123


Output

1.000000000000

Note

In the first sample we need either win no tour or win the third one. If we win nothing we wouldn't perform well. So, we must to win the third tour. Other conditions will be satisfied in this case. Probability of wining the third tour is 0.3.

In the second sample we win the only tour with probability 1.0, and go back home with bag for it.

Solution (in JAVA):

Solution:

import java.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.Vector;

/**
 * 4 4
 * 1 5 3 4
 * 1 2
 * 1 3
 * 2 3
 * 3 3
 *
 *
 * @author pttrung
 */
public class A {

    public static long Mod = (long) (1e9) + 7;
    static int[] X = {0, -1, 0, 1};
    static int[] Y = {-1, 0, 1, 0};
    static boolean ok = true;

    public static void main(String[] args) throws FileNotFoundException {
        PrintWriter out = new PrintWriter(System.out);
        //PrintWriter out = new PrintWriter(new FileOutputStream(new File("output.txt")));
        Scanner in = new Scanner();
        int n = in.nextInt();
        int l = in.nextInt();
        int k = Math.min(in.nextInt(), n);
        Prize[] data = new Prize[n];
        for (int i = 0; i < n; i++) {
            data[i] = new Prize(in.nextInt(), 0, 0);
        }
        int c = 0;
        for (int i = 0; i < n; i++) {
            int v = in.nextInt();
            data[i].b = v;
            if (v < 0) {
                c++;
            } else {
                data[i].t = 1;
            }
        }
        Arrays.sort(data, new Comparator<Prize>() {
            @Override
            public int compare(Prize o1, Prize o2) {
                return o1.t - o2.t;
            }
        });
      //  System.out.println(Arrays.toString(data));
        double[][] p = new double[n + 1][n + 1];//Bag + Win
        p[k][0] = 1;
        for (int i = c; i < n; i++) {
            for (int j = n; j >= 0; j--) {
                for (int h = n - 1; h >= 0; h--) {
                    if (p[j][h] > 0) {
                        double v = (double) data[i].p / 100;
                        int nxt = Math.min(data[i].b + j, n);
                        p[nxt][h + 1] += v * p[j][h];
                        p[j][h] *= (1 - v);
                    }
                }
            }
        }
        
        for (int i = n - 1; i >= 0; i--) {
            for (int j = n; j >= 0; j--) {


                p[i][j] += p[i + 1][j];
                
            }
        }

        double[][] o = new double[n + 1][n + 1];//Prize + win
        o[0][0] = 1;
        for (int i = 0; i < c; i++) {
            for (int j = n - 1; j >= 0; j--) {
                for (int h = n - 1; h >= 0; h--) {
                    if (o[j][h] > 0) {
                        double v = (double) data[i].p / 100;
                        o[j + 1][h + 1] += v * o[j][h];
                        o[j][h] *= (1 - v);
                    }
                }
            }
        }
        double total = 0;
        for (int i = l; i <= n; i++) {
            for (int j = 0; j <= i; j++) {
                for (int h = 0; h <= i; h++) {
                    total += o[j][h] * p[j][i - h];
                }
            }
        }
        out.println(total);




        out.close();
    }

    static class Prize {

        int p, b, t;

        public Prize(int p, int b, int t) {
            this.p = p;
            this.b = b;
            this.t = t;
        }

        @Override
        public String toString() {
            return "Prize{" + "p=" + p + ", b=" + b + ", t=" + t + '}';
        }
    }

    static long[] extendEuclid(long a, long b) {
        if (b == 0) {
            return new long[]{a, 1, 0};
        }
        long[] re = extendEuclid(b, a % b);
        long x = re[2];
        long y = re[1] - (a / b) * re[2];
        re[1] = x;
        re[2] = y;
        return re;

    }

    static long[] modularLinearSolver(long a, long b, long n) {
        long[] ex = extendEuclid(a, n);
        if (b % ex[0] != 0) {
            throw new IllegalArgumentException("No solution");
        }
        long[] result = new long[(int) n];
        result[0] = (ex[1] * (b / ex[0])) % n;
        for (int i = 1; i < ex[0]; i++) {
            result[i] = result[0] + i * (n / ex[0]);
        }
        return result;
    }

    static int[] KMP(String v) {
        int i = 0, j = -1;

        int[] result = new int[v.length() + 1];
        result[0] = -1;
        while (i < v.length()) {
            while (j >= 0 && v.charAt(i) != v.charAt(j)) {
                j = result[j];
            }
            i++;
            j++;
            result[i] = j;
        }
        return result;
    }

    static int find(int index, int[] u) {
        if (index != u[index]) {
            return u[index] = find(u[index], u);
        }
        return index;
    }

    public static long pow(int a, int b, long mod) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long v = pow(a, b / 2, mod);
        if (b % 2 == 0) {
            return (v * v) % mod;
        } else {
            return (((v * v) % mod) * a) % mod;
        }
    }

    public static int[][] powSquareMatrix(int[][] A, long p) {
        int[][] unit = new int[A.length][A.length];
        for (int i = 0; i < unit.length; i++) {
            unit[i][i] = 1;
        }
        if (p == 0) {
            return unit;
        }
        int[][] val = powSquareMatrix(A, p / 2);
        if (p % 2 == 0) {
            return mulMatrix(val, val);
        } else {
            return mulMatrix(A, mulMatrix(val, val));
        }

    }

    public static int[][] mulMatrix(int[][] A, int[][] B) {
        int[][] result = new int[A.length][B[0].length];
        for (int i = 0; i < result.length; i++) {
            for (int j = 0; j < result[0].length; j++) {
                long temp = 0;
                for (int k = 0; k < A[0].length; k++) {

                    temp += ((long) A[i][k] * B[k][j] % Mod);
                    temp %= Mod;
                }
                temp %= Mod;
                result[i][j] = (int) temp;
            }
        }

        return result;
    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;




    }

    static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        void update(int index, int val) {
            // System.out.println("UPDATE INDEX " + index);
            while (index < data.length) {
                data[index] += val;
                index += index & (-index);

                //    System.out.println("NEXT " +index);
            }
        }

        long get(int index) {
            //  System.out.println("GET INDEX " + index);
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= index & (-index);
                // System.out.println("BACK " + index);
            }
            return result;
        }

        public String toString() {
            return Arrays.toString(data);
        }
    }

    static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        } else {
            return gcd(b, a % b);
        }
    }

    static long pow(long a, int b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {

            return val * val % Mod;
        } else {
            return (val * val % Mod) * a % Mod;
        }
    }

//    static Point intersect(Point a, Point b, Point c) {
//        double D = cross(a, b);
//        if (D != 0) {
//            return new Point(cross(c, b) / D, cross(a, c) / D);
//        }
//        return null;
//    }
//
//    static Point convert(Point a, double angle) {
//        double x = a.x * cos(angle) - a.y * sin(angle);
//        double y = a.x * sin(angle) + a.y * cos(angle);
//        return new Point(x, y);
//    }
    static Point minus(Point a, Point b) {
        return new Point(a.x - b.x, a.y - b.y);
    }
//
//    static Point add(Point a, Point b) {
//        return new Point(a.x + b.x, a.y + b.y);
//    }
//

    /**
     * Cross product ab*ac
     *
     * @param a
     * @param b
     * @param c
     * @return
     */
    static double cross(Point a, Point b, Point c) {
        Point ab = new Point(b.x - a.x, b.y - a.y);
        Point ac = new Point(c.x - a.x, c.y - a.y);
        return cross(ab, ac);
    }

    static double cross(Point a, Point b) {
        return a.x * b.y - a.y * b.x;
    }

    /**
     * Dot product ab*ac;
     *
     * @param a
     * @param b
     * @param c
     * @return
     */
    static long dot(Point a, Point b, Point c) {
        Point ab = new Point(b.x - a.x, b.y - a.y);
        Point ac = new Point(c.x - a.x, c.y - a.y);
        return dot(ab, ac);
    }

    static long dot(Point a, Point b) {
        long total = a.x * b.x;
        total += a.y * b.y;
        return total;
    }

    static double dist(Point a, Point b) {
        long total = (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
        return Math.sqrt(total);
    }

    static long norm(Point a) {
        long result = a.x * a.x;
        result += a.y * a.y;
        return result;
    }

    static double dist(Point a, Point b, Point x, boolean isSegment) {
        double dist = cross(a, b, x) / dist(a, b);
        // System.out.println("DIST " + dist);

        if (isSegment) {
            Point ab = new Point(b.x - a.x, b.y - a.y);

            long dot1 = dot(a, b, x);
            long norm = norm(ab);
            double u = (double) dot1 / norm;
            if (u < 0) {
                return dist(a, x);
            }

            if (u > 1) {
                return dist(b, x);
            }
        }
        return Math.abs(dist);




    }

    static long squareDist(Point a, Point b) {
        long x = a.x - b.x;
        long y = a.y - b.y;
        return x * x + y * y;
    }

    static class Point {

        int x, y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public String toString() {
            return "Point{" + "x=" + x + ", y=" + y + '}';
        }

        @Override
        public int hashCode() {
            int hash = 7;
            hash = 19 * hash + this.x;
            hash = 19 * hash + this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            //System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //br = new BufferedReader(new FileReader(new File("input.txt")));
        }

        public String next() {


            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}