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 *s*<sub class="lower-index">*i*</sub> — 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.
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 *s*<sub class="lower-index">*i*</sub> (1 ≤ *s*<sub class="lower-index">*i*</sub> ≤ 100), denoting the number of students in the *i*-th department. Note that *s*<sub class="lower-index">*h*</sub> includes Herr Wafa.
3 2 1
2 1
1
3 2 1
1 1
-1
3 2 1
2 2
0.666667
3 2 1
1 2
0.000000
6 5 3
5 2 3 10 5
0.380435
7 10 6
9 10 2 3 3 6 9 9 3 7
0.420946
17 5 1
10 4 9 6 2
0.999860
5 8 3
9 7 2 5 2 10 3 4
0.097561
14 8 4
6 2 10 6 2 8 4 2
0.885750
14 9 9
9 4 7 2 1 2 4 3 9
0.971132
46 73 68
4 2 6 4 1 9 8 10 7 8 7 2 6 4 7 9 7 9 9 1 5 1 5 1 8 2 10 2 1 7 10 2 8 3 5 3 8 9 10 5 3 4 10 4 9 6 8 1 1 6 3 1 9 6 9 4 4 3 4 5 8 1 6 2 4 10 5 7 2 6 7 4 2
0.525158
24 55 54
8 3 6 4 8 9 10 2 2 6 6 8 3 4 5 6 6 6 10 4 8 2 3 2 2 2 10 7 10 1 6 1 6 8 10 9 2 8 9 6 6 4 1 2 7 2 2 9 3 7 3 7 6 8 4
0.433479
63 25 24
6 7 7 1 2 5 5 9 9 1 9 8 1 2 10 10 5 10 2 9 5 4 9 5 7
0.891560
44 94 2
2 4 10 9 5 1 9 8 1 3 6 5 5 9 4 6 6 2 6 2 4 5 7 3 8 6 5 10 2 1 1 9 1 9 3 1 9 6 2 4 9 7 4 6 1 4 5 2 7 8 2 1 1 1 4 2 5 5 5 8 2 8 2 1 1 8 1 7 7 7 1 2 5 3 8 9 8 7 2 10 5 2 2 8 9 1 4 7 7 2 6 2 8 5
0.259627
44 35 7
10 2 2 6 4 2 8 3 10 1 9 9 7 9 10 6 6 1 4 5 7 4 9 7 10 10 7 9 6 1 7 7 2 10 7
0.793743
27 47 44
8 5 2 5 10 6 7 9 5 10 8 5 9 5 10 5 10 8 5 1 1 2 2 10 3 2 5 9 6 3 3 1 5 4 10 5 2 2 4 4 4 4 4 1 1 3 7
0.000000
21 67 49
4 4 3 5 7 5 10 2 8 5 2 2 6 3 6 2 8 6 2 6 2 9 3 3 4 1 9 9 3 3 6 3 6 7 8 9 10 6 10 5 1 5 2 3 3 9 10 5 10 7 1 6 4 5 4 7 8 5 4 2 9 3 3 5 7 1 10
0.414860
42 71 67
2 1 4 1 10 5 1 8 8 5 2 1 1 7 2 2 8 10 8 2 10 8 2 2 9 6 5 10 7 1 7 2 10 3 5 6 10 10 4 6 10 5 6 6 9 4 1 6 1 8 10 6 1 5 3 2 4 1 8 5 10 10 9 3 10 7 5 9 1 9 3
0.362240
50 93 28
2 5 9 5 5 8 1 3 9 2 7 10 3 1 10 10 8 5 2 7 5 4 3 9 5 2 8 9 10 8 2 7 8 9 8 1 9 8 4 3 3 6 10 10 1 2 10 1 8 10 5 8 5 2 4 1 5 6 9 8 6 7 4 6 6 1 5 1 4 6 8 4 1 7 2 8 7 5 1 3 3 7 4 2 1 5 7 5 8 3 8 7 2
0.563739
33 90 4
5 10 2 3 9 6 9 3 3 8 6 4 8 4 9 3 5 9 5 6 4 1 10 6 4 5 4 5 9 5 7 1 3 9 6 6 5 6 2 4 8 7 8 5 4 5 10 9 3 1 1 8 6 9 5 1 5 9 4 6 6 4 9 4 5 7 3 7 9 1 5 6 4 1 1 4 2 4 4 2 6 4 5 5 4 9 1 10 2 2
0.132213
65 173 136
26 18 8 11 1 22 44 6 15 22 13 49 30 36 37 41 25 27 9 36 36 1 45 20 7 47 28 30 30 21 33 32 9 11 16 5 19 12 44 40 25 40 32 36 15 34 4 43 28 19 29 33 7 11 18 13 40 18 10 26 1 48 20 38 1 20 34 8 46 8 32 35 16 49 26 36 11 16 4 29 35 44 14 21 22 42 10 1 3 12 35 30 14 45 2 24 32 15 2 28 35 17 48 31 7 26 44 43 37 4 14 26 25 41 18 40 15 32 16 7 40 22 43 8 25 21 35 21 47 45 7 21 50 38 23 13 4 49 10 27 31 38 43 40 10 24 39 35 31 33 9 6 15 18 2 14 20 14 12 12 29 47 9 49 25 17 41 35 9 40 19 50 34
0.165731
77 155 26
15 18 38 46 13 15 43 37 36 28 22 26 9 46 14 32 20 11 8 28 20 42 38 40 31 20 2 43 1 42 25 28 40 47 6 50 42 45 36 28 38 43 31 14 9 22 49 4 41 9 24 35 38 40 19 31 4 9 13 19 15 48 2 34 46 49 41 15 13 29 15 24 15 50 8 26 10 23 24 15 2 46 47 46 25 36 41 29 44 36 24 22 41 7 48 17 42 41 4 46 15 26 48 27 35 19 35 22 47 7 40 1 15 46 6 34 44 6 9 5 29 24 5 25 12 38 46 10 35 12 8 15 1 9 1 16 2 12 24 31 37 49 27 41 33 5 26 48 42 37 20 18 49 40 16
0.299854
67 108 14
33 40 13 10 26 31 27 24 48 1 42 28 38 29 9 28 48 41 12 19 27 50 6 45 46 7 34 47 8 18 40 27 42 4 33 3 10 25 10 29 39 3 5 39 1 17 40 10 6 8 41 50 27 43 40 42 43 25 18 34 6 15 5 9 11 37 13 4 16 25 49 33 14 40 13 16 50 24 4 43 45 12 31 38 40 36 3 4 4 19 18 12 20 44 4 44 8 50 21 5 44 34 9 9 6 39 43 21
0.504558
82 135 73
22 18 8 45 35 8 19 46 40 6 30 40 10 41 43 38 41 40 1 43 19 23 5 13 29 16 30 9 4 42 42 3 24 16 21 26 5 4 24 24 31 30 1 10 45 50 33 21 21 47 42 37 47 15 30 23 4 2 28 15 38 33 45 30 31 32 6 14 6 4 39 12 50 29 26 45 19 12 40 4 33 9 16 12 44 36 47 42 43 17 18 12 12 42 45 38 6 10 19 10 14 31 6 21 2 15 21 26 5 3 3 6 6 22 44 48 9 11 33 31 34 43 39 40 48 26 1 29 48 11 22 38 23 11 20
0.706768
73 121 102
11 21 12 1 48 30 22 42 42 35 33 12 23 11 27 15 50 49 24 2 48 2 21 32 16 48 36 26 32 13 38 46 36 15 27 24 7 21 43 49 19 13 3 41 35 17 5 22 42 19 37 20 40 42 11 31 48 16 21 5 42 23 29 44 9 30 46 21 44 27 9 17 39 24 30 33 48 3 43 18 16 18 17 46 19 26 37 5 24 36 42 12 18 29 7 49 1 9 27 12 21 29 19 38 6 19 43 46 33 42 9 30 19 38 25 10 44 23 50 25 46
0.470538
50 113 86
2 17 43 22 48 40 42 47 32 29 10 4 9 14 20 50 8 29 12 11 50 41 3 22 30 4 48 37 27 19 50 50 23 34 13 21 3 36 31 39 22 27 7 21 31 21 14 18 36 19 27 42 19 8 5 41 7 8 22 40 38 32 44 25 21 48 4 12 10 16 23 30 25 41 16 45 3 26 19 34 34 25 26 6 9 21 46 33 36 45 3 13 28 44 30 29 22 41 20 1 20 38 4 33 36 15 41 18 13 11 13 18 6
0.298885
74 146 112
10 31 40 32 9 17 31 26 32 7 20 18 50 10 15 28 6 41 21 27 11 5 14 36 48 45 10 42 45 40 4 11 41 23 47 31 34 4 42 49 48 9 37 34 25 27 30 27 44 33 30 25 22 13 25 41 8 34 32 22 11 12 32 9 37 9 42 7 37 13 20 40 28 26 2 6 2 49 41 46 11 9 32 18 43 28 39 48 45 36 18 10 28 35 26 5 20 12 16 2 34 28 31 13 18 39 40 1 39 12 33 31 1 31 46 1 47 38 39 49 32 12 2 8 16 27 48 41 16 27 38 42 21 27 26 8 31 41 20 43 47 5 39 25 47 34
0.437111
78 124 41
5 28 46 46 13 48 36 2 28 31 31 12 9 28 40 35 34 50 50 30 17 11 6 36 16 30 29 8 18 16 21 8 15 30 29 20 12 5 29 20 11 44 12 42 49 10 11 7 25 15 2 38 30 29 17 34 4 5 44 49 25 15 16 33 26 8 8 34 21 9 33 16 14 8 43 50 45 17 15 43 44 22 37 36 22 47 6 13 49 48 37 44 50 9 35 13 38 31 15 6 35 48 22 14 18 8 40 18 4 23 2 26 41 41 27 40 43 33 2 17 11 40 42 32
0.218709
51 153 26
19 32 28 7 25 50 22 31 29 39 5 4 28 26 24 1 19 23 36 2 50 50 33 28 15 17 31 35 10 40 16 7 6 43 50 29 20 25 31 37 10 18 38 38 44 30 36 47 37 6 16 48 41 49 14 16 30 7 29 42 36 8 31 37 26 15 43 42 32 3 46 12 16 37 33 12 18 16 15 14 46 11 2 50 34 34 34 32 28 24 44 12 9 38 35 12 11 15 2 6 28 35 14 46 25 30 9 1 26 5 35 26 4 32 2 30 36 29 22 4 5 1 44 38 6 48 48 6 43 45 24 19 44 18 37 18 40 45 25 35 20 27 21 29 43 18 26 46 22 39 29 41 1
0.183488
100 10 5
10 8 7 5 8 1 2 4 3 10
-1
100 10 8
1 8 9 7 6 4 4 6 8 5
-1
1 1 1
1
0.000000
1 1 1
2
0.000000
1 1 1
100
0.000000
100 1 1
100
1
99 1 1
100
1
100 2 1
100 1
1
#!/usr/bin/env python3

from math import factorial


def c(n, k):
    if k < 0 or k > n:
        return 0
    else:
        return factorial(n) / factorial(k) / factorial(n - k)


def main():
    n, _, h = list(map(int, input().split()))
    s = list(map(int, input().split()))

    if sum(s) < n:
        print(-1)
    else:
        print(c(sum(s) - s[h - 1], n - s[h - 1]) / c(sum(s) - 1, n - 1))

if __name__ == '__main__':
    main()
