Week 0 ~ mixedcows.X Each of Farmer Ran's N (4 <= N <= 16) cows has a unique serial number S_i (1 <= S_i <= 25,000). The cows are so proud of it that each one now wears her number engraved in large letters on a plate hung around her ample bovine neck. These cows are unusual in that they line up to be milked in an order called 'Mixed Up'. A cow order is 'Mixed Up' if the sequence of serial numbers formed by their milking line is such that the serial numbers of every pair of consecutive cows in line differs by more than K (1 <= K <= 3400). For example, if N = 6 and K = 1 then 1, 3, 5, 2, 6, 4 is a 'Mixed Up' lineup but 1, 3, 6, 5, 2, 4 is not (since the consecutive numbers 5 and 6 differ by 1). How many different ways can N cows be Mixed Up? PROBLEM NAME: mixedcows.X INPUT FORMAT: * Line 1: Two space-separated integers: N and K * Lines 2..N+1: Line i+1 contains a single integer that is the serial number of cow i: S_i SAMPLE INPUT: 4 1 3 4 2 1 OUTPUT FORMAT: * Line 1: A single integer that is the number of ways that N cows can be 'Mixed Up'. The answer is guaranteed to fit in a 64 bit integer. SAMPLE OUTPUT: 2 OUTPUT DETAILS: The 2 possible Mixed Up arrangements are: 3 1 4 2 2 4 1 3