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.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.text.NumberFormat;
import java.util.Scanner;

/**
 * 题意：一个团队需要 n 个人，学校有 m 个系(编号：1-m)，主人公在 h 系； 
 * 		第二行输入 s[i] 表示第 i 系的人数(包括主人公自己)。
 * 		在所有系中随机挑选 n 个人，问跳出的人中存在和主人公所在同一系的概率。
 * 
 * C(下标,上标)、sum 表示全校人数 
 * 分析：P(团队中没有人和主人公在同一个系) = (在全校总人数-h系人数中选出n-1人)/(在全校人数-1中选择n-1人) 
 * 即：C(sum-s[h],n-1)/C(sum-1,n-1) = A(s-s[h],n-1)/A(s-1,n-1) 
 * 结果 = 1 - p(不在同一个系) = 1 - A(s-s[h],n-1)/A(s-1,n-1);
 * 
 * @author dolphinzhou
 *
 */
public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		int teamNum; // 团队所需人数
		int departmentNum; // 系的数量
		int currentDepart; // 主人公所在系编号
		int studentSum; // 学校总人数
		int currentDepartNum; // 主人公所在系的人数
		while (in.hasNext()) {
			teamNum = in.nextInt();
			departmentNum = in.nextInt();
			currentDepart = in.nextInt();
			currentDepartNum = 0;
			studentSum = 0;
			int temp;
			// 记录主人公所在系的人数以及全校总人数
			for (int index = 1; index <= departmentNum; index++) {
				temp = in.nextInt();
				studentSum += temp;
				if (index == currentDepart) {
					currentDepartNum = temp;
				}
			}
			if (studentSum < teamNum) {
				out.println(-1);
			} else if (teamNum == 1) {
				out.println(0);
			} else {
				// 计算 A(s-s[h],n-1)/A(s-1,n-1)
				BigDecimal denominator = BigDecimal.valueOf(studentSum - 1); // 分母
				BigDecimal member = BigDecimal.valueOf(studentSum - currentDepartNum); // 分子
				BigDecimal tempBD1 = denominator;
				BigDecimal tempBD2 = member;
				while (teamNum-- > 2) {
					tempBD1 = tempBD1.subtract(BigDecimal.valueOf(1));
					denominator = denominator.multiply(tempBD1);
					tempBD2 = tempBD2.subtract(BigDecimal.valueOf(1));
					member = member.multiply(tempBD2);
				}
				// 注意此处：大浮点数相除，除不断时，会报异常。所以需要设置结果长度以及四舍五入的方法
				double ans = 1 - member.divide(denominator, 6, BigDecimal.ROUND_HALF_UP).doubleValue();
				NumberFormat numberFormat = NumberFormat.getInstance();
				// 设置数值的小数部分允许的最大位数
				numberFormat.setMaximumFractionDigits(6);
				// 去掉小数后面多余的零
				out.println(numberFormat.format(ans));
			}
		}
		out.flush();
	}
}
