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,raw_input().split())
s = map(int,raw_input().split())
result = 0
lap = s[0]
for i in xrange(1,n):
    #print s[i],lap
    if s[i]<lap:
        a = (lap-s[i])/d+1
    elif s[i]==lap:
        a = 1
    else:
        a = 0
    result += a
    lap = s[i]+d*a
    #print a,lap
    #print '--------'
print int(result)




