As a German University in Cairo (GUC) student and a basketball player, Herr Wafa was delighted once he heard the news. GUC is finally participating in the Annual Basketball Competition (ABC). 

A team is to be formed of n players, all of which are GUC students. However, the team might have players belonging to different departments. There are m departments in GUC, numbered from 1 to m. Herr Wafa's department has number h. For each department i, Herr Wafa knows number si — how many students who play basketball belong to this department.

Herr Wafa was also able to guarantee a spot on the team, using his special powers. But since he hates floating-point numbers, he needs your help at finding the probability that he will have at least one teammate belonging to his department. 

Note that every possible team containing Herr Wafa is equally probable. Consider all the students different from each other.

Input

The first line contains three integers n, m and h (1 ≤ n ≤ 100, 1 ≤ m ≤ 1000, 1 ≤ h ≤ m) — the number of players on the team, the number of departments in GUC and Herr Wafa's department, correspondingly. 

The second line contains a single-space-separated list of m integers si (1 ≤ si ≤ 100), denoting the number of students in the i-th department. Note that sh includes Herr Wafa.

Output

Print the probability that Herr Wafa will have at least one teammate from his department. If there is not enough basketball players in GUC to participate in ABC, print -1. The answer will be accepted if it has absolute or relative error not exceeding 10 - 6.

Examples

Input

3 2 1
2 1


Output

1


Input

3 2 1
1 1


Output

-1


Input

3 2 1
2 2


Output

0.666667

Note

In the first example all 3 players (2 from department 1 and 1 from department 2) must be chosen for the team. Both players from Wafa's departments will be chosen, so he's guaranteed to have a teammate from his department.

In the second example, there are not enough players.

In the third example, there are three possibilities to compose the team containing Herr Wafa. In two of them the other player from Herr Wafa's department is part of the team.


import java.awt.Point;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import static java.lang.Math.*;

public class ProblemD_83 {
	
	final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE")!=null;
	BufferedReader in;
	PrintWriter out;
	StringTokenizer tok = new StringTokenizer("");
	
	void init() throws FileNotFoundException{
		if (ONLINE_JUDGE){
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
		}else{
			in = new BufferedReader(new FileReader("input.txt"));
			out = new PrintWriter("output.txt");
		}
	}
	
	String readString() throws IOException{
		while(!tok.hasMoreTokens()){
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}
	
	int readInt() throws IOException{
		return Integer.parseInt(readString());
	}
	
	long readLong() throws IOException{
		return Long.parseLong(readString());
	}
	
	double readDouble() throws IOException{
		return Double.parseDouble(readString());
	}
	
	public static void main(String[] args){
		new ProblemD_83().run();
	}
	
	public void run(){
		try{
			long t1 = System.currentTimeMillis();
			init();
			solve();
			out.close();
			long t2 = System.currentTimeMillis();
			System.err.println("Time = "+(t2-t1));
		}catch (Exception e){
			e.printStackTrace(System.err);
			System.exit(-1);
		}
	}
	
	static class Utils {

		private Utils() {}

		public static void mergeSort(int[] a) {
			mergeSort(a, 0, a.length - 1);
		}

		private static void mergeSort(int[] a, int leftIndex, int rightIndex) {
			final int MAGIC_VALUE = 50;
			if (leftIndex < rightIndex) {
				if (rightIndex - leftIndex <= MAGIC_VALUE) {
					insertionSort(a, leftIndex, rightIndex);
				} else {
					int middleIndex = (leftIndex + rightIndex) / 2;
					mergeSort(a, leftIndex, middleIndex);
					mergeSort(a, middleIndex + 1, rightIndex);
					merge(a, leftIndex, middleIndex, rightIndex);
				}
			}
		}

		private static void merge(int[] a, int leftIndex, int middleIndex, int rightIndex) {
			int length1 = middleIndex - leftIndex + 1;
			int length2 = rightIndex - middleIndex;
			int[] leftArray = new int[length1];
			int[] rightArray = new int[length2];
			System.arraycopy(a, leftIndex, leftArray, 0, length1);
			System.arraycopy(a, middleIndex + 1, rightArray, 0, length2);
			for (int k = leftIndex, i = 0, j = 0; k <= rightIndex; k++) {
				if (i == length1) {
					a[k] = rightArray[j++];
				} else if (j == length2) {
					a[k] = leftArray[i++];
				} else {
					a[k] = leftArray[i] <= rightArray[j] ? leftArray[i++] : rightArray[j++];
				}
			}
		}

		private static void insertionSort(int[] a, int leftIndex, int rightIndex) {
			for (int i = leftIndex + 1; i <= rightIndex; i++) {
				int current = a[i];
				int j = i - 1;
				while (j >= leftIndex && a[j] > current) {
					a[j + 1] = a[j];
					j--;
				}
				a[j + 1] = current;
			}
		}

	}
	
	void solve() throws IOException{
		
		int n = readInt() - 1;
		int m = readInt();
		int h = readInt() - 1;
		long s = 0;
		long sh = 0;
		for (int i = 0; i < m; i++){
			if (i == h) sh = readLong() - 1;
			else s += readLong();
		}
		if (s + sh < n){
			out.print(-1);
			return;
		}
		if (sh == 0 || n == 0){
			out.print(0);
			return;
		}
		double[] p = new double[n];
		p[0] = (double) s / (s + sh);
		for (int i = 1; i < n; i++){
			p[i] = p[i-1] * (s - i) / (s + sh - i);
		}
		out.printf(Locale.US, "%.8f", 1 - p[n-1]);
	}
	
	static int[][] step8 = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}, {-1, -1}, {1, -1}, {-1, 1}, {1, 1}};
	
	static int[][] stepKnight = {{-2, -1}, {-2, 1}, {-1, -2}, {-1, 2}, {1, -2}, {1, 2}, {2, -1}, {2, 1}};
	
	static long gcd(long a, long b){
		if (a == 0)	return b;
		return gcd(b % a, a);
	}
	
	static long lcm(long a, long b){
		return a / gcd(a, b)*b;
	}

	static long[] gcdPlus(long a, long b){
		long[] d = new long[3];
		if (a == 0){
			d[0] = b;
			d[1] = 0;
			d[2] = 1;
		}else{
			d = gcdPlus(b % a, a);
			long r = d[1];
			d[1] = d[2] - b/a*d[1];
			d[2] = r;
		}
		return d;
	}
	
	static long binpow(long a, int n){
		if (n == 0)	return 1;
		if ((n & 1) == 0){
			long b = binpow(a, n/2);
			return b*b;
		}else return binpow(a, n - 1)*a;
	}
	
	static long binpowmod(long a, int n, long m){
		if (m == 1) return 0;
		if (n == 0)	return 1;
		if ((n & 1) == 0){
			long b = binpowmod(a, n/2, m);
			return (b*b) % m;
		}else return binpowmod(a, n - 1, m)*a % m;
	}
	
	static long phi(long n){
		int[] p = Sieve((int)ceil(sqrt(n)) + 2);
		long phi = 1;
		for (int i = 0; i < p.length; i++){
			long x = 1;
			while (n % p[i] == 0){
				n /= p[i];
				x *= p[i];
			}
			phi *= x - x/p[i];
		}
		if (n != 1) phi *= n - 1;
		return phi;
	}
	
	static long f(long n, int x, int k){ //���-�� ���������� ����� (������� 0), ���������� � ���� ����� �� 0 �� k-1
		if (n == 0)	return 1;
		long b = binpow(10, x - 1);
		long c = n / b;
		return (c < k? c: k)*binpow(k, x - 1) + (c < k? 1: 0)*f(n % b, x - 1, k);
	}
	
	static long fib(int n){
		if (n == 0) return 0;
		if ((n & 1) == 0){
			long f1 = fib(n/2 - 1);
			long f2 = fib(n/2 + 1);
			return f2*f2 - f1*f1;
		}else{
			long f1 = fib(n/2);
			long f2 = fib(n/2 + 1);
			return f1*f1 + f2*f2;
		}
	}
	
	static BigInteger BigFib(int n){
		if (n == 0) return BigInteger.ZERO;
		if ((n & 1) == 0){
			BigInteger f1 = BigFib(n/2 - 1);
			f1 = f1.multiply(f1);
			BigInteger f2 = BigFib(n/2 + 1);
			f2 = f2.multiply(f2);
			return f2.subtract(f1);
		}else{
			BigInteger f1 = BigFib(n/2);
			f1 = f1.multiply(f1);
			BigInteger f2 = BigFib(n/2 + 1);
			f2 = f2.multiply(f2);
			return f2.add(f1);
		}
	}
	
	static public class PointD{
		
		double x, y;
		
		public PointD(double x, double y){
			this.x = x;
			this.y = y;
		}
	}
	
	static double d(Point p1, Point p2){
		return sqrt(d2(p1, p2));
	}
	
	static public double d(PointD p1, PointD p2){
		return sqrt(d2(p1, p2));
	}
	
	static double d2(Point p1, Point p2){
		return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);
	}
	
	static public double d2(PointD p1, PointD p2){
		return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);
	}
	
	static boolean IsProbablyPrime(long n){
		if (n == 1)	return false;
		if ((n & 1) == 0) return false;
		for (int j = 3; j < sqrt(n) + 1; j += 2){
			if (n % j == 0)	return false;
		}
		return true;
	}

	static int[] Sieve(int n){
		boolean[] b = new boolean[n+1];
		Arrays.fill(b, true);
		b[0] = false;
		b[1] = false;
		long nLong = n;
		int j=0;
		for (int i = 1; i <= n; i++) {
			if (b[i]){
				j++;
				if (((long)i)*i <= nLong) {
					for (int k = i*i; k <= n; k += i) {
						b[k] = false;
					}
				}
			}
		}
		int[] p = new int[j];
		Arrays.fill(p, 0);
		j=0;
		for (int i = 2; i <= n; i++) {
			if (b[i]){
				p[j]=i;
				j++;
			}
		}
		return p;
	}
	
	static int[][] Palindromes(String s){
		char[] c = s.toCharArray();
		int n = c.length;
		int[][] d = new int[2][n];
		int l = 0, r = -1;
		for (int i = 0; i < n; i++){
			int j = (i > r? 0: min(d[0][l+r-i+1], r-i+1)) + 1;
			for (; i - j >= 0 && i + j - 1< n && c[i-j] == c[i+j-1]; j++);
			d[0][i] = --j;
			if (i + d[0][i] - 1 > r){
				r = i + d[0][i] - 1;
				l = i - d[0][i];
			}
		}
		l = 0;
		r = -1;
		for (int i = 0; i < n; i++){
			int j = (i > r? 0: min(d[1][l+r-i], r-i)) + 1;
			for (; i - j >= 0 && i + j < n && c[i-j] == c[i+j]; j++);
			d[1][i] = --j;
			if (i + d[1][i] > r){
				r = i + d[1][i];
				l = i - d[1][i];
			}
		}
		return d;
	}
	
	static public class Permutation {
		
		int[] a;
		int n;
		
		public Permutation(int n){
			this.n=n;
			a=new int[n];
			for (int i=0; i<n; i++){
				a[i]=i;
			}
		}
		
		public boolean nextPermutation(){ //������� � do{}while(nextPermutation(a));
			int i=n-1;
			for (i=n-2; i>=0; i--){
				if (a[i]<a[i+1]){
					break;
				}
			}
			if (i==-1){
				return false;
			}
			int jMin=i+1;
			for (int j=n-1; j>i; j--){
				if (a[i]<a[j]&&a[j]<a[jMin]){
					jMin=j;
				}
			}
			swap(i, jMin);
			for (int j=1; j<=(n-i)/2; j++){
				swap(i+j, n-j);
			}
			return true;
		}
		
		
		public int get(int i){
			return a[i];
		}
		
		void swap(int i, int j){
			int r=a[i];
			a[i]=a[j];
			a[j]=r;
		}
	}
	
	static public class Fraction implements Comparable<Fraction>, Cloneable{
		
		public final Fraction FRACTION_ZERO = new Fraction();
		public final Fraction FRACTION_ONE = new Fraction(1);
		public long numerator = 0;
		public long denominator = 1;
		
		public Fraction(){
			numerator = 0;
			denominator = 1;
		}
		
		public Fraction(long numerator){
			this.numerator = numerator;
			denominator = 1;
		}
		
		public Fraction(long numerator, long denominator){
			this.numerator = numerator;
			this.denominator = denominator;
			Cancellation();
		}
		
		public Fraction(double numerator, double denominator, int accuracy){
			this.numerator = (long)(numerator*pow(10,accuracy));
			this.denominator = (long)(denominator*pow(10,accuracy));
			Cancellation();
		}
		
		public Fraction(String s){
			if (s.charAt(0) == '-'){
				denominator = -1;
				s = s.substring(1);
			}
			if (s.indexOf("/") != -1){
				denominator *= Integer.parseInt(s.substring(s.indexOf("/") + 1));
			}
			if (s.indexOf(" ") != -1){
				numerator = Integer.parseInt(s.substring(0, s.indexOf(" "))) * abs(denominator) + Integer.parseInt(s.substring(s.indexOf(" ") + 1, s.indexOf("/")));
			}else{
				if (s.indexOf("/") != -1){
					numerator = Integer.parseInt(s.substring(0, s.indexOf("/")));
				}else{
					numerator = Integer.parseInt(s)*abs(denominator);
				}
			}
			this.Cancellation();
		}
		
		void Cancellation(){
			long g = gcd(abs(numerator), abs(denominator));
			numerator /= g;
			denominator /= g;
			if (denominator < 0){
				numerator *= -1;
				denominator *= -1;
			}
		}
		
		public String toString(){
			String s = "";
			if (numerator == 0){
				return "0";
			}
			if (numerator < 0){
				s += "-";
			}
			if (abs(numerator) >= denominator){
				s += Long.toString(abs(numerator) / denominator) + " ";
			}
			if (abs(numerator) % denominator != 0){
				s += Long.toString(abs(numerator) % denominator);
			}else{
				s = s.substring(0, s.length()-1);
			}
			if (denominator != 1){
				s += "/" + Long.toString(denominator);
			}
			return s;
		}
		
		public Fraction add(Fraction f){
			Fraction fResult = new Fraction();
			fResult.denominator = lcm(denominator, f.denominator);
			fResult.numerator = numerator * fResult.denominator / denominator + f.numerator * fResult.denominator / f.denominator;
			fResult.Cancellation();
			return fResult;
		}
		
		public Fraction subtract(Fraction f){
			Fraction fResult = new Fraction();
			fResult.denominator = lcm(denominator, f.denominator);
			fResult.numerator = numerator * fResult.denominator / denominator - f.numerator * fResult.denominator / f.denominator;
			fResult.Cancellation();
			return fResult;
		}
		
		public Fraction multiply(Fraction f){
			Fraction fResult = new Fraction();
			fResult.numerator = numerator * f.numerator;
			fResult.denominator = denominator * f.denominator;
			fResult.Cancellation();
			return fResult;
		}
		
		public Fraction divide(Fraction f){
			Fraction fResult = new Fraction();
			fResult.numerator = numerator * f.denominator;
			fResult.denominator = denominator * f.numerator;
			fResult.Cancellation();
			return fResult;
		}
		
		@Override
		public int compareTo(Fraction f){
			long g = gcd(denominator, f.denominator);
			long res = numerator * (f.denominator / g) - f.numerator * (denominator / g);
			if (res < 0){
				return -1;
			}
			if (res > 0){
				return 1;
			}
			return 0;
		}
		
		public Fraction clone(){
			Fraction fResult = new Fraction(numerator, denominator);
			return fResult;
		}
		
		public Fraction floor(){
			Fraction fResult = this.clone();
			fResult.numerator = (fResult.numerator / fResult.denominator) * fResult.denominator;
			return fResult;
		}
		
		public Fraction ceil(){
			Fraction fResult = this.clone();
			fResult.numerator = (fResult.numerator/fResult.denominator + 1) * fResult.denominator;
			return fResult;
		}
		
		public Fraction binpow(int n){
			if (n==0) return FRACTION_ONE;
			if ((n&1)==0){
				Fraction f=this.binpow(n/2);
				return f.multiply(f);
			}else return binpow(n-1).multiply(this);
		}
	}
	
	static public class FenwickTree_1{	//One-dimensional array		
		
		int n;
		long[] t;
		
		public FenwickTree_1(int n){
			this.n = n;
			t = new long[n];
		}
		
		public long sum(int xl, int xr){
			return sum(xr) - sum(xl);
		}
		
		public long sum(int x){
			long result = 0;
			for (int i = x; i >= 0; i = (i & (i + 1)) - 1){
				result += t[i];
			}
			return result;
		}
		
		public void update(int x, long delta){
			for (int i = x; i < n; i = (i | (i + 1))){
				t[i] += delta;
			}
		}
	}
	
	static public class FenwickTree_2{	//Two-dimensional array
		
		int n, m;
		long[][] t;
		
		public FenwickTree_2(int n, int m){
			this.n = n;
			this.m = m;
			t = new long[n][m];
		}
		
		public long sum(int xl, int yl, int xr, int yr){
			return sum(xr, yr) - sum(xl - 1, yr) - sum(xr, yl - 1) + sum(xl - 1, yl - 1);
		}
		
		public long sum(int x, int y){
			long result = 0;
			for (int i = x; i >= 0; i = (i & (i + 1)) - 1){
				for (int j = y; j >= 0; j = (j & (j + 1)) - 1){
					result+=t[i][j];
				}
			}
			return result;
		}
		
		public void update(int x, int y, long delta){
			for (int i = x; i < n; i = (i | (i + 1))){
				for (int j = y; j < m; j = (j | (j + 1))){
					t[i][j] += delta;
				}
			}
		}
	}
	
	static public class FenwickTree_3{	//Three-dimensional array
		
		int n, m, l;
		long[][][] t;
		
		public FenwickTree_3(int n, int m, int l){
			this.n = n;
			this.m = m;
			this.l = l;
			t = new long[n][m][l];
		}
		
		public long sum(int xl, int yl, int zl, int xr, int yr, int zr){
			return sum(xr, yr, zr) - sum(xl - 1, yr, zr)
			+ sum(xl - 1, yr, zl - 1) - sum(xr, yr, zl - 1)
			- sum(xr, yl - 1, zr) + sum(xl - 1, yl - 1, zr)
			- sum(xl - 1, yl - 1, zl - 1) + sum(xr, yl - 1, zl - 1);
		}
		
		public long sum(int x, int y, int z){
			long result = 0;
			for (int i = x; i >= 0; i = (i & (i + 1)) - 1){
				for (int j = y; j >= 0; j = (j & (j + 1)) - 1){
					for (int k = z; k >= 0; k = (k & (k + 1)) - 1){
						result += t[i][j][k];
					}
				}
			}
			return result;
		}
		
		public void update(int x, int y, int z, long delta){
			for (int i = x; i < n; i = (i | (i + 1))){
				for (int j = y; j < n; j = (j | (j + 1))){
					for (int k = z; k < n; k = (k | (k + 1))){
						t[i][j][k] += delta;
					}
				}
			}
		}
	}
}

