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
'''
Jana Goodman6

11A Increasing Sequence

'''
import math
SPACE = ' '

def min_moves(n, d, b):
    result = 0
    for i in range(0, n - 1):
        if b[i+1] <= b[i]:
            times = abs(b[i+1] - b[i]) // d + 1
            b[i+1] += d * times
            result += times
    return result

if __name__ == '__main__':
    n, d = map(int, input().split(SPACE))
    b = list(map(int, input().split(SPACE)))
    print(min_moves(n, d, b))
