Problem Statement

There is a row of $L$ chairs. Now, $N$ groups of people will come and take seats in order. Each group consists of one or two people, and the $i$-th group to come consists of $a_i$ people. The total number of people equals $L$.

Each group will randomly choose unoccupied chairs where all group members can sit consecutively, and occupy those chairs. However, if there are not enough consecutive unoccupied chairs, they will leave without taking seats.

Determine whether it is guaranteed that all $N$ groups can take seats.

Constraints

• $1\leq N\leq 2\times 10^5$
• $1\leq a_i\leq 2$
• $L=a_1 +a_2 +\ldots +a_N$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N L
a_1 a_2 \ldots a_N

Output

If it is guaranteed that all $N$ groups can take seats, print Yes; otherwise, print No.