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

import math

def main( ):
    n, d = map( int, input( ).split( ) )
    b = list( map( int, input( ).split( ) ) )
    # n, d = 2000, 1
    # b = [ 1 ] * 2000

    moves = 0

    for i in range( n ):
        if i == 0: continue
        if b[ i ] <= b[ i - 1 ]:
            m = math.ceil( ( b[ i - 1 ] + 1 - b [ i ] ) / d )
            moves += m
            b[ i ] += m * d

    print( moves )

if __name__ == '__main__':
    main( )

