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
X = list(map(int, input().split()))
Numbers = list(map(int, input().split()))
Moves = 0
for i in range(1, X[0]):
    if Numbers[i] <= Numbers[i - 1]:
        Now = (Numbers[i - 1] - Numbers[i]) // X[1] + 1
        Moves += Now
        Numbers[i] += X[1] * Now
print(Moves)

# UB_CodeForces
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