Description

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

There are T test cases(2≤T≤20). The frist line of each test case contains two integer numbers n and d (2≤n≤2000,1≤d≤10^6). The second line contains space separated sequence b0,b1,...,bn-1 (1≤bi≤10^6).

Output

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

Sample

Input

4 2
1 3 3 2

Output

3