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
def increasing (b,d):
    m = 0
    for x in range(1,len(b)):
        if b[x] <= b[x-1] :
            dif = b[x-1] - b[x]
            if dif == 0:
                m += 1
                b[x] += d
            else:
                m += dif//d + 1
                b[x] += d*((dif//d)+1)
            
    return m

n,d = list(map(int,input().split()))
b = list(map(int,input().split()))

print (increasing(b,d))
