Problem Statement

michirakara has finally reached his long-awaited goal of a rating in the $3200$s on AtCoder.

On AtCoder, users with a rating of $3200$ or higher can display their name in any color they like.

michirakara wants to display his name in a certain color $M$.

However, michirakara has no sense of style, so the only way he can make a color is by mixing two colors.

The color obtained by mixing colors $A$ and $B$ is $\left\lfloor\cfrac{A+B}{2}\right\rfloor$.

michirakara wants the color of his name to be $M$.

michirakara's initial color is $L$.

Given $L$ and $N$ colors $A_1,A_2,\dots ,A_N$, print Yes if the color $M$ can be made by mixing colors, and No otherwise.

Each of the colors $A_1,A_2,\dots ,A_N$ can either be used for mixing, or be left unused so that the current color is kept.

The $N$ colors are mixed in order from $A_1$ to $A_N$.

For example, it is possible to mix $A_1$, skip $A_2$, and then mix $A_3$, but it is not possible to mix $A_1$ after mixing $A_3$.

Input

$N\ M \ L$
$A_1\ A_2\dots A_N$

• $1\leq N\leq 100$
• $1\leq M\leq 1000$
• $1\leq L\leq 1000$
• $1\leq A_i\leq 1000(1\leq i\leq N)$
• All inputs are integers.

Sample

5 10 5
9 10 13 14 12

Yes

5 10 5
1 2 8 4 7

No

1 5 5
1

Yes