A sequence a0,a1,...,at-1 is called increasing if ai-1 \lt ai for each i:0 \lt i \lt t.

You are given a sequence b0,b1,...,bn-1 and a positive integer d. In each move you may choose one element of the given sequence and add d to it. What is the least number of moves required to make the given sequence increasing?

The first line of the input contains two integer numbers n and d (2 \le n \le 2000,1 \le d \le 106). The second line contains space separated sequence b0,b1,...,bn-1 (1 \le bi \le 106).

Output the minimal number of moves needed to make the sequence increasing.