A sequence a, a, …, a[N-1] is called decreasing if a[i] >= a[i+1] for each i: 0 <= i < N-1. You are given a sequence of numbers a, a,…, a[N-1] and a positive integer K. In each 'operation', you may subtract K from any element of the sequence. You are required to find the minimum number of 'operations' to make the given sequence decreasing.
The first line contains a positive integer T denoting the number of test cases. Each of the test case consists of 2 lines. The first line of each test case contains two integers N and K. Next line contains space separated sequence of N integers.
Output the minimum number of ‘operations’ for each case on new line.Print your answer modulo 109+7.
1 <= T <=100
1 <= N <= 106
1 <= K <= 100 1 <= a <= 103
For 1st case: One operation is required to change a = 2 into -3 and two opertations are required to change a = 3 into -7. The resulting sequence will be 1 1 -3 -7. Hence, in total 3 operations are required.
For 2nd and 3rd cases: The sequence is already decreasing. Hence, no operations are required in both the cases.