monkey-and-stone

As Lord Rama's army is approaching Lanka they have to pass one last hurdle and that is the ocean in between. They have decided to construct a bridge made of stones. But before they start constructing it Lord Rama asked Hanuman to train the monkeys in the army.

Hanuman decided to train monkeys with the following strategy.

Monkeys stand in a straight line along the x-axis with their faces in the positive y-direction. Each monkey is given a stone.

Each monkey throws his stone to either left or right along the line.

When two stones traveling with the same speed collide they just reverse their directions and continue to move in the new direction. 

Each stone travel with the same speed of 1 unit per second.
Assume that the radius of stone is zero and can be treated as a point.

Each monkey can decide direction(left or right) for his stone with equal probability. At time t = 0, Hanuman blows his horn and each monkey throws his stone in the chosen direction.To measure their performance Hanuman decided to find the expected number of collisions in a give time T seconds(including the collision at T second). 

Help Hanuman to find this value.

Input:

You will be given an integer N  denoting the number of monkeys in the line and an integer T denoting the time.

Next line will contain N non-negative integers denoting the position of monkeys.

Output:

Output a single line containing the value Hanuman decided to calculate.

Constraint:

0 < N ≤ 20

0 < T ≤ 100000000 (10^8)

0 ≤ Position of Monkey ≤ 100000000 (10^8)

SAMPLE INPUT
2 2
5 8

SAMPLE OUTPUT
0.25

Source: hackerearth | Difficulty: UNKNOWN_DIFFICULTY


Solutions: