Simon is a contestant on the new exciting game show, Add ’Em Up! In this show, contestants are given a set of cards with multi-digit numbers on them, and need to select two cards that add up to a given sum. However, to make things more interesting, the font that the cards are printed in (see below) means that certain cards will display different numbers if turned upside-down, and it is legal to turn either or both of the cards if necessary to generate the sum. Please help Simon win the game!

-----Input-----
The first line contains two integers, $n$, the number of cards, and $s$, the desired sum. The second line will contain $n$ integers between $1$ and $100000000$ inclusive. You may assume that $1\leq n\leq 100000$ and $2\leq s\leq 200000000$.

-----Output-----
The output should be a single line consisting of the string YES if two cards can be chosen such that (in some orientation) they add up to $s$, and the string NO otherwise.

-----Examples-----
Sample Input:
3 66
15 21 22
Sample Output:
NO

Source: kattis | Difficulty: MEDIUM


Solutions: