Gifts
Santa Claus has brought N boxes of candies for the New Year's party. At the celebration, there are K_1+K_2 children. Among them, K_1 children prefer to receive an even number of candies, while K_2 children prefer an odd number.
Santa Claus aims to distribute all the boxes such that each child receives at least one box, and their preference for the parity of candies is respected. Note that boxes cannot be opened, and candies from one box cannot be divided among multiple children.
Input
The first line of the input contains three integers: N, K_1, and K_2 (1 ≤ N, K_1, K_2 ≤ 10^5). The second line contains N integers a_i, where each a_i represents the number of candies in the corresponding box (1 ≤ a_i ≤ 10^9).
Output
Output a single line containing "YES" if Santa Claus can distribute all the boxes to satisfy the children's preferences, or "NO" if he cannot.