Problem Statement

Tonight, Takeya entered a yakitori restaurant in Shinjuku's "Omoide Yokocho" to have a drink. At this restaurant, it seems you can take part in a drinking contest under the following rules.

・The owner and Takeya take turns drinking sake
・There are N types of sake
・On your turn, choose one type of sake and drink 1 to K (integer) (ml) of it
・Whoever cannot drink sake loses

Note that both the owner and Takeya have a very high tolerance for alcohol, so consider "cannot drink sake" ⇔ "there is no sake left".

Takeya moves first. The amount of each sake is given. Assuming that each player does their best, determine whether Takeya can win this contest.

Output "YES" if Takeya can win, and "NO" if he loses.



(☆) I wish I could have gone to a restaurant called Asadachi in "Omoide Yokocho". It is a place where you can eat so-called bizarre dishes such as raw pig testicle sashimi.

Input

$N$ $K$
$A_1$ $A_2$ $\dots$ $A_{N}$

$1 \leq N \leq 1000$
$1 \leq K \leq 1000$
$0 \leq A_{i} \leq 1000000$

$N$: the number of types of sake
$K$: the maximum amount that can be drunk in $1$ turn. Choose any integer $t$ from the K integers $1, 2, \dots,K$ and drink exactly t (ml)
$A_{i}$: the initial amount (ml) of sake $i$

Output

Assuming that both players do their best, output "YES" if Takeya can win, and "NO" if he loses.

Sample

3 10
0 0 0

NO

5 1
0 0 0 2 0

NO

2 5
11 13

YES

4 30
134 12 500 15000

YES