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
import sys
import math

n, d = [int(x) for x in (sys.stdin.readline()).split()]
bn = [int(x) for x in (sys.stdin.readline()).split()]

res = 0
for i in range(n - 1):
    if(bn[i] > bn[i + 1]):
        z = bn[i] - bn[i + 1]
        k = int(z / d) + 1
        res += k
        bn[i + 1] += d * k
    elif(bn[i] == bn[i + 1]):
        bn[i + 1] += d
        res += 1
        
if(bn[n - 2] >= bn[n - 1]):
    z = bn[n - 2] - bn[n - 1]
    k = int(z / d) + 1
    res += k
elif(bn[n - 2] >= bn[n - 1]):
    res += 1
     
print(res)
        