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, input().split())
a = list(map(int, input().split()))
l = 0
ans = 0

for i in range(n):
    if l >= a[i]:
        t, s = divmod((l-a[i]+1), d)
        if s:
            t += 1
        if not(t):
            t += 1
        a[i] += d*t
        ans += t
    l = a[i]

print(ans)
        
