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
#!/usr/bin/env python
# -*- coding: utf-8 -*-

from math import ceil

def main():
    n, d = map(int, raw_input().split())
    ns = map(float, raw_input().split())
    c = 0
    for i in xrange(1, n):
        if ns[i] < ns[i-1]:
            dc = int(ceil((ns[i-1] - ns[i]) / d))
            ns[i] += dc*d
            c += dc
        if ns[i] == ns[i-1]:
            ns[i] += d
            c += 1
    print c
    return 0

if __name__ == '__main__':
    main()
