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
var lll = readline().split(' ')
var N = +lll[0]
var D = +lll[1]

var ns = readline().split(' ').map(function (i) {return parseInt(i)})

var sn = 0

for (var i = 1; i < N; i++) {
  var dif = ns[i] - ns[i - 1]
  if (dif <= 0) {
    var inc = (-dif / D | 0) + 1
    sn += inc
    ns[i] += D * inc
  }
}

print(sn)