A7781. Increasing Sequence

A sequence $a_{0},a_{1},...,a_{t-1}$ is called increasing if $a_{i-1}<a_{i}$ for each $i:0<i<t$ .

You are given a sequence $b_{0},b_{1},...,b_{n-1}$ 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 $d$ ( $2<=n<=2000,1<=d<=10^{6}$ ). The second line contains space separated sequence $b_{0},b_{1},...,b_{n-1}$ ( $1<=b_{i}<=10^{6}$ ).

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