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
n,d = map(int,raw_input().strip().split())

B = map(int,raw_input().strip().split())
count = 0
for i in range(1,n):
    val = 0
    #print B
    if B[i] <= B[i-1]:
        diff = B[i-1] - B[i] + 1
        #print diff,d
        if diff%d:
            val = diff/d + 1

        
        else:
            val = diff/d
        
        count += val  
        B[i] += val*d

print count       
