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
f =input().split()
n = int(f[0])
d = int(f[1])
s = 0
g = input().split()
a = int(g[0])
for i in range(1,n):
    a1 = int(g[i])
    if (a >= a1):
        s += ((a - a1) // d) + 1
        a1 += ((a - a1) // d) * d + d
    a = a1
print(s)