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
#!/usr/bin/env python3

n, d = [int(j) for j in input().split(' ')]
a = [int(j) for j in input().split(' ')]
steps = 0
for i in range(n):
    if (i+1 < n):
        if a[i] >= a[i+1]:
            step = int((a[i] - a[i+1])/d) + 1
            a[i+1] += step*d
            steps += step
        else:
            continue
    else:
        break

print(steps)
