Given an array and an integer , you are tasked to find the longest subsequence of the array . A subsequence is if and only if none of the products of neighbouring elements in the subsequence exceed . That is, suppose is the subsequence of with length , is if and only if for any , where , .
Note: An array is a subsequence of another array if can be created by removing some elements (possibly none) from array without changing the order of elements. For example, the array is a subsequence of , whereas the array and the array is \textbf{not} a subsequence of .
输入格式
The first line contains two space-seperated integers, () and () -- is the length of array and is the integer given.
The second line contains space-seperated integers, ().
输出格式
The only line contains an integer, which is the length of the longest subsequence.
样例
样例输入 1
1 10
100
样例输出 1
1
样例输入 2
5 10
3 4 2 5 1
样例输出 2
4
样例输入 3
5 10
6 -2 -2 -6 5
样例输出 3
4
数据范围与提示
Note
A subsequence of one element is always valid because there are no neighbouring elements. Therefore, the length of the longest subsequence is .
This example has a subsequence, . It is because the product of the neighbouring elements does not exceed , as shown below.
The subsequence (i.e., the original array ) is because the product of the first and second elements is 12, which exceeds .
Therefore, the length of the longest subsequence is .
The longest subsequence is .
The subsequence (i.e., the original array ) is because the product of the third and fourth elements is , which exceeds .
