Pillow Stacking

Eleanor recently lost her favorite pillow. She is very particular about her pillows and sorts them by softness. The pillow she lost had softness $C$, and she cannot sleep without this exact softness. She has access to several other types of pillows, but none of them may have softness $C$. To work around this, she sleeps on a stack of multiple pillows.

When pillows with softness $C_1, C_2, \ldots, C_k$ are stacked in that order, the resulting softness is

$C_1 + \left\lceil \frac{C_2}{2} \right\rceil + \left\lceil \frac{C_3}{4} \right\rceil + \cdots + \left\lceil \frac{C_k}{2^{k-1}} \right\rceil$

In other words, the $i$th pillow contributes $2^{-(i-1)}$ of its softness, rounded up. $\lceil f \rceil$ is the smallest integer $x$ with $x \geq f$.

Eleanor has plenty of money and can use an unlimited number of each pillow type she has access to. Determine whether she can stack pillows to reach softness $C$.

The first line contains two integers $N$ and $C$ ($1 \leq N \leq 10^3$, $1 \leq C \leq 10^4$). $N$ is the number of pillow types Eleanor has access to, and $C$ is the desired softness. The next line contains $N$ integers $a_1, a_2, \ldots, a_N$ ($1 \leq a_i \leq 10^{18}$), the softness of each pillow type.

If Eleanor can stack pillows to reach softness $C$, print YES. Otherwise, print NO.