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
def main():
    n, d = map(int, input().split())
    b = [int(c) for c in input().split()]
    b.append(float('infinity'))
    res = 0
    for i in range(len(b) - 1):
        curr, prev = b[i+1], b[i]
        if curr <= prev:
            curr_diff = curr - prev
            target_diff = 1
            div, mod = divmod(target_diff - curr_diff, d)
            moves = div if mod == 0 else div + 1
            res += moves
            b[i+1] += moves * d

    print(res)
    
if __name__ == '__main__':
    main()
