Maximizing Consecutive Piles

Bytie received a set of identical wooden blocks and arranged them in n piles in a row. His father then challenged him with the following puzzle:

Given an integer threshold h, rearrange the blocks using only the following move so that the number of consecutive piles having at least h blocks is maximized.

The allowed move is: from any pile i with number of blocks a[i] satisfying $$a_i > h,$$ remove the top block (thus setting a[i] := a[i] - 1) and place it atop one of the piles immediately adjacent to it (either i-1 or i+1, if such a pile exists) so that a[j] := a[j] + 1.

Restrictions:

• You are not allowed to form any new piles; blocks may only be moved among the existing ones.
• You can perform as many moves as you wish, in any order.

Your task is to compute the maximum length of a contiguous segment of piles that can be made to have at least h blocks each after some sequence of allowed moves.

Note: Since moves are allowed only from piles with more than h blocks, once a pile reaches exactly h it cannot donate any block further. For simplicity, assume that the number of piles is small.

inputFormat

The input consists of two lines:

• The first line contains two integers n and h where 1 ≤ n ≤ 10. Here, n is the number of piles and h is the threshold number of blocks.
• The second line contains n integers a[1], a[2], ..., a[n] (each at most 10) representing the initial numbers of blocks in the piles.

outputFormat

Output a single integer — the maximum possible length of a contiguous segment of piles that can be made to have at least h blocks each after performing any sequence of allowed moves.

sample

5 3
2 4 1 3 3

2