Decreasing Sequence
Submissions: 431   Accuracy:


  Difficulty: Easy   Marks: 2

A sequence a[0], a[1], …, 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[0], a[1],…, 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

4 5
1 1 2 3
5 2
5 4 3 2 1
5 3
5 4 3 3 1



For 1st case: One operation is required to change a[2] = 2 into -3 and two opertations are required to change a[3] = 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.

** For More Input/Output Examples Use 'Expected Output' option **

Contributor: Sajal Agrawal
Author: sajalagrawal

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