You are given an array nums of positive integers and a target. You need to return the length of the longest subsequence whose elements sum exactly to target.

However, you must manage a cooldown mechanic: every time you include an element nums[i] in your subsequence, you are forbidden from including any of the next k elements from the original array in your subsequence, where k = nums[i] % 4.

Find the maximum length of a valid subsequence. If no valid subsequence exists that sums exactly to target, return -1.

Input Format

• The first line contains an integer, N, denoting the size of the array.
• The second line contains an integer, target, denoting the required sum.
• The third line contains N space-separated integers denoting the N positive integers nums.

Constraints

• $1 \le N \le 1000$
• $1 \le target \le 1000$
• $1 \le nums[i] \le 1000$