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
import sys
import math
import bisect

def solve(A, d):
    n = len(A)
    ans = 0
    for i in range(1, n):
        if A[i] <= A[i-1]:
            delta = A[i-1] + 1 - A[i]
            k = (delta + d - 1) // d
            A[i] += k * d
            ans += k
    return ans

def main():
    n, d = map(int, input().split())
    A = list(map(int, input().split()))
    ans = solve(A, d)
    print(ans)

if __name__ == "__main__":
    main()
