you are given an array **A** of $$$n$$$ positive integers ( $$$0<A[i]<10^9$$$ ) and $$$r$$$ moves.

on each move: you can choose any subarray of **A** (which contains only positive elements) and decrease all elements in that subarray by one.

your task is to maximize the number of $$$0$$$ values in your array.

print that number after $$$r$$$ moves.

**input:**

$$$n,r$$$

$$$A[1],A[2],..A[n]$$$

**ouput:**

- number of $$$0$$$ values after r moves

**example input:**

$$$6$$$ $$$2$$$

$$$0$$$ $$$2$$$ $$$1$$$ $$$2$$$ $$$2$$$ $$$3$$$

**output**

$$$4$$$

**subtask1:**$$$n<=10;r=1$$$**subtask2:**$$$n<=10;r<=5$$$**subtask3:**$$$n<=200;r<=200$$$**subtask4:**$$$n<=200;r<=10^9$$$**subtask5:**$$$n<=2000;r<=10^9$$$