A sequence a0,a1,...,at-1 is called increasing if ai-1<ai for each i:0<i<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?

Input

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

Output

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

Examples

Input

4 2
1 3 3 2

Output

3

意思:

如果後一項小於等於前一項，就把d加上當前元素，使得陣列遞增。輸出最少加多少個2.