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A. Increasing Sequence

time limit per test

1 secondmemory limit per test

64 megabytesinput

standard inputoutput

standard outputA 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?

Input

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

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

Examples

Input

4 2

1 3 3 2

Output

3

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