Petrol Queue

You are given an array a representing the petrol distribution of the petrol queue of \(n\) vehicles. The \(0 th\) position of the array represents the front of the queue. There is a limited amount of petrol liters available in the shed. The manager of the petrol shed wants to distribute the petrol in non-increasing order so the vehicles at the back never get more petrol than vehicles at the front.

But the pump attendant distributes the petrol the way he wants. So the manager asks you to make the distribution non-increasing by doing the following operation a minimum number of times.

• Remove 1 liter from \(i^{th}\) vehicle and pump 1 liter to the \(j^{th}\) vehicle \((a_i-1,a_j+1)\) OR
• Remove 1 liter from \(j^{th}\) vehicle and pump 1 liter to the \(i^{th}\) vehicle \((a_j-1,a_i+1)\).

Your task is to find the minimum number of operations needed to make the petrol distribution non-increasing. There can be vehicles that do not get any petrol at all.

Input Format

First line contains two integers \(n\) and \(m\), \(n\) - number of vehicles in the petrol queue, \(m\) - available amount of petrol in liters

Second line contains \(n\) integers \(a_0,a_1,a_2,...,a_{n-1}\) representing the petrold distribution among the vehicles by the pump attendant. Sum of these \(n\) integers equal to \(m\).

Output Format

Print a single integer representing the minimum number of operations required to make the petrol distribution non-increasing.

Constraints

Limits

• Time Limit: 1s
• Memory Limit: 256MB

Sample Input 0

6 13
4 2 1 2 2 2

Sample Output 0

2

Sample Input 1

3 9
4 3 2

Sample Output 1

0

Sample Input 2

2 1
0 1

Sample Output 2

1