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
len,add = map(int, input().split())

liste = list(map(int,input().split()))
num = 0
i = 0

while(i < len - 1):
    if ( liste[i] < liste[i + 1]):
        i +=1
    elif( liste[i] == liste[i + 1]):
        liste[i + 1] += add
        i += 1
        num +=1

    else:
        val = (liste[i] - liste[i + 1])/add
        m = int(val)
        if(val >= m): m += 1
        liste[i + 1] += m * add
        num += m
        i += 1

print(num)


