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: $$$n<=2000;r<=10^9$$$