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.
#include <bits/stdc++.h>
using namespace std;
long long null = 0;
struct segment;
struct line;
struct point;
struct vec;
struct ray;
struct point {
  long double x, y;
  point() {}
  point(long double x1, long double y1) {
    x = x1;
    y = y1;
  }
  long double dist_to_point(point p) {
    return sqrt((p.x - x) * (p.x - x) + (p.y - y) * (p.y - y));
  }
  bool operator<(point p) { return (x < p.x) || ((x == p.x) && (y < p.y)); }
};
struct vec {
  long double x, y;
  vec(long double x1, long double y1) {
    x = x1;
    y = y1;
  }
  vec(point a, point b) {
    x = b.x - a.x;
    y = b.y - a.y;
  }
  vec normal() {
    vec ans;
    ans.x = y;
    ans.y = -x;
    return ans;
  }
  vec opposite() {
    vec ans;
    ans.x = -x;
    ans.y = -y;
    return ans;
  }
  vec sum(vec b) {
    vec ans;
    ans.x = x + b.x;
    ans.y = y + b.y;
    return ans;
  }
  long double cross_product(vec v) { return x * v.y - v.x * y; }
  long double dot_product(vec v) { return x * v.x + y * v.y; }
  vec resize(long double size) {
    vec ans;
    ans.x = (x * size) / len();
    ans.y = (y * size) / len();
    return ans;
  }
  vec() {}
  long double len() { return sqrt(x * x + y * y); }
};
struct line {
  long double a, b, c;
  line(point a1, point b1) {
    a = a1.y - b1.y;
    b = b1.x - a1.x;
    c = -a1.x * a - a1.y * b;
  }
  line(long double a1, long double b1, long double c1) {
    a = a1;
    b = b1;
    c = c1;
  }
  line() {}
  vec normal_vec() {
    vec ans;
    ans.x = a;
    ans.y = b;
    return ans;
  }
  line normal_line(point p) {
    line ans;
    ans.a = -b;
    ans.b = a;
    ans.c = -ans.a * p.x - ans.b * p.y;
    return ans;
  }
  long double get_x(long double y1) {
    if (a == 0) return 0;
    return (-c - b * y1) / a;
  }
  long double get_y(long double x1) {
    if (b == 0) return 0;
    return (-c - a * x1) / b;
  }
  point intersection(line l) {
    point ans;
    ans.x = (-c * l.b + l.c * b) / (a * l.b - l.a * b);
    ans.y = (-a * l.c + l.a * c) / (a * l.b - l.a * b);
    return ans;
  }
  bool parallels(line l) { return a * l.b - l.a * b == 0; }
  long double dist_to_point(point p) {
    return abs((a * p.x + b * p.y + c) / (sqrt(a * a + b * b)));
  }
  long long is_inside(point p) {
    long double k = a * p.x + b * p.y + c;
    if (k < 0)
      return -1;
    else if (k == 0)
      return 0;
    return 1;
  }
};
struct segment {
  point a, b;
  segment() {}
  segment(point a1, point b1) {
    a = a1;
    b = b1;
  }
  long double len() {
    return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
  }
  bool is_inside(point p) {
    line l(a, b);
    if (l.is_inside(p) != 0) return false;
    vec v(p, a), v1(p, b);
    if (v.dot_product(v1) > 0) return false;
    return true;
  }
  long double dist_to_point(point p) {
    vec v(a, p), v1(a, b), v2(b, p), v3(b, a);
    if (v.dot_product(v1) < 0) return p.dist_to_point(a);
    if (v2.dot_product(v3) < 0) return p.dist_to_point(b);
    line l(a, b);
    return l.dist_to_point(p);
  }
  point get_center() {
    point ans;
    ans.x = (a.x + b.x) / 2;
    ans.y = (a.y + b.y) / 2;
    return ans;
  }
};
struct ray {
  point a, b;
  ray(point p, point p1) {
    a = p;
    b = p1;
  }
  ray() {}
  long double dist_to_point(point p) {
    vec v(a, p), v1(a, b);
    if (v.dot_product(v1) < 0) return a.dist_to_point(p);
    line l(a, b);
    return l.dist_to_point(p);
  }
  bool is_inside(point p) {
    line l(a, b);
    if (l.is_inside(p) != 0) return false;
    vec v(a, p), v1(a, b);
    if (v.dot_product(v1) < 0) return false;
    return true;
  }
};
struct angle {
  point a, b, c;
  angle(){};
  angle(point a1, point b1, point c1) {
    a = a1;
    b = b1;
    c = c1;
  }
  long double get_angle() {
    vec v(b, a), v1(b, c);
    return acos(v.dot_product(v1) / (v.len() * v1.len()));
  }
  long double get_grad_angle() {
    vec v(b, a), v1(b, c);
    return 180 * acos(v.dot_product(v1) / (v.len() * v1.len())) /
           3.141592653589793238462643;
  }
};
struct polygon {
  long long n;
  vector<point> points;
  long double get_area() {
    point a(0, 0);
    vec v(a, points[0]);
    long double ans = 0;
    for (long long i = 1; i < n; ++i) {
      vec v1(a, points[i]);
      ans = ans + v.cross_product(v1);
      v = v1;
    }
    vec v2(a, points[0]);
    vec v1(a, points[n - 1]);
    return abs(ans + v1.cross_product(v2)) / 2;
  }
};
struct triangle {
  point a, b, c;
  triangle() {}
  triangle(point a1, point b1, point c1) {
    a = a1;
    b = b1;
    c = c1;
  }
  long double get_area() {
    point d(0, 0);
    vec v(a, d), v1(b, d), v2(c, d);
    return (v.cross_product(v1) + v1.cross_product(v2) + v2.cross_product(v)) /
           2;
  }
  point get_center() {
    segment s(a, b), s1(a, c);
    point p = s.get_center(), p1 = s1.get_center();
    line l(a, b), l1(a, c), l2(b, c);
    l = l.normal_line(p);
    l1 = l1.normal_line(p1);
    return l.intersection(l1);
  }
  long double get_R() {
    triangle t(a, b, c);
    point p = t.get_center();
    return p.dist_to_point(a);
  }
};
long long power(long long a, long long b) {
  if (b == 0)
    return 1;
  else if (b == 1)
    return a;
  else {
    long long k = power(a, b / 2);
    return k * k * power(a, b % 2);
  }
}
long long power_mod(long long a, long long b, long long MOD) {
  if (b == 0)
    return 1;
  else if (b == 1)
    return a % MOD;
  else {
    long long k = power_mod(a, b / 2, MOD);
    return ((k * k) % MOD * power_mod(a, b % 2, MOD)) % MOD;
  }
}
long long sum_mod(long long a, long long b, long long MOD) {
  return (a + b) % MOD;
}
long long mul_mod(long long a, long long b, long long MOD) {
  return (a * b) % MOD;
}
long long ord(char a) { return a; }
char chr(long long a) { return a; }
long long strtoint(string s) {
  long long ans = 0;
  for (long long i = 0; i < s.size(); ++i) {
    ans *= 10;
    ans += ord(s[i]) - 48;
  }
  return ans;
}
string rev_string(string s) {
  string ans = "";
  for (long long i = s.size(); i >= 0; --i) {
    ans += s[i];
  }
  return ans;
}
string inttostr(long long a) {
  string ans = "", ans1 = "";
  while (a > 0) {
    ans += chr(a + 48);
    a /= 10;
  }
  for (long long i = ans.size() - 1; i >= 0; --i) {
    ans1 += ans[i];
  }
  return ans1;
}
long long gcd(long long a, long long b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
long long nok(long long a, long long b) { return a * b / gcd(a, b); }
long long ar[20000];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  srand(time(0));
  long long n, m, h, s = 0;
  long double ans = 1;
  cin >> n >> m >> h;
  for (long long i = 0; i < m; ++i) {
    cin >> ar[i];
    s += ar[i];
  }
  if (s < n) {
    cout << -1;
    exit(0);
  }
  --h;
  --s;
  --ar[h];
  for (long long i = 1; i < n; ++i) {
    ans *= (s - ar[h]) * 1.0 / s;
    --s;
  }
  cout << fixed << setprecision(20) << 1 - ans;
}
