{"raw_statement":[{"iden":"problem statement","content":"You have a circle of length $C$, and you are placing $N$ arcs on it. Arc $i$ has length $L_i$.\nEvery arc $i$ is placed on the circle uniformly at random: a random real point on the circle is chosen, then an arc of length $L_i$ centered at this point appears.\nNote that the arcs are placed independently. For example, they may intersect or contain each other.\nWhat is the probability that every real point of the circle will be covered by at least one arc? Assume that an arc covers its ends."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 6$\n*   $2 \\leq C \\leq 50$\n*   $1 \\leq L_i < C$\n*   All input values are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $C$\n$L_1$ $L_2$ $...$ $L_N$"},{"iden":"sample input 1","content":"2 3\n2 2"},{"iden":"sample output 1","content":"0.3333333333333333\n\nThe centers of the two arcs must be at distance at least $1$. The probability of this on a circle of length $3$ is $1 / 3$."},{"iden":"sample input 2","content":"4 10\n1 2 3 4"},{"iden":"sample output 2","content":"0.0000000000000000\n\nEven though the total length of the arcs is exactly $C$ and it's possible that every real point of the circle is covered by at least one arc, the probability of this event is $0$."},{"iden":"sample input 3","content":"4 2\n1 1 1 1"},{"iden":"sample output 3","content":"0.5000000000000000"},{"iden":"sample input 4","content":"3 5\n2 2 4"},{"iden":"sample output 4","content":"0.4000000000000000"},{"iden":"sample input 5","content":"4 6\n4 1 3 2"},{"iden":"sample output 5","content":"0.3148148148148148"},{"iden":"sample input 6","content":"6 49\n22 13 27 8 2 19"},{"iden":"sample output 6","content":"0.2832340720702695"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}