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()) #n: Número de elementos, d:Número a agregar
    sec = list(map(int, input().split())) #Secuancia
    ans = 0
        
    for i in range(1,n): 
        while sec[i] <= sec[i-1]:
            need = (sec[i-1] - sec[i]) // d #Enteros necesarios para llegar a lo necesario
            
            if need < 1: need = 1
            
            sec[i] = sec[i] + (d * need)
            ans += need
            
    print(ans)
        


if __name__ == "__main__":
    main()
    
    
