C. Kero ! Kero ! El3ab ya Kero !
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

$$$Mohamed$$$ and $$$Kero$$$ are playing a game during their spare time.

they are given an array $$$A$$$ of length $$$N$$$ and an integer $$$K$$$.

in the game, $$$Mohamed$$$ will play first then $$$Kero$$$.

$$$Mohamed$$$ will choose any index $$$i$$$ $$$(1 \leq i \leq N)$$$, and add to his score $$$(a_i \% K)$$$, and according to these steps each one of them tries to maximize his score.

Help us to find if $$$Mohamed$$$ will win the game or not.

Note : each $$$a_i$$$ is used once.

Input

First line , Given two integers $$$N$$$, $$$K$$$ . $$$(1 \leq N \leq 2*10^5)$$$ , $$$(1 \leq K \leq 10^9)$$$, $$$N$$$ is the length of array $$$A$$$ and $$$K$$$.

Second line, Given an array $$$A$$$ of $$$N$$$ integers , $$$(-10^9 \leq a_i \leq 10^9)$$$.

Output

if $$$Mohamed$$$ is the winner, print "YES", otherwise print "NO" in any form (Yes/yES/YeS)( No/nO/no).

Examples
Input
3 5
2 9 -7
Output
YES
Input
4 4
1 -3 7 -9
Output
NO
Note

A $$$\%$$$ K = ((A $$$\%$$$ K) + K) $$$\%$$$ K .

in the first test case :

step $$$1$$$ : $$$Mohamed$$$ will choose $$$(i=2)$$$ then $$$( 9 \% 5 = 4)$$$ then $$$Mohamed$$$ score $$$= 4.$$$

step $$$2$$$ : $$$Kero$$$ will choose $$$(i=3)$$$ then $$$( -7 \% 5 = 3)$$$ then $$$Kero$$$ score $$$= 3.$$$

step $$$3$$$ : $$$Mohamed$$$ will choose $$$(i=1)$$$ then $$$( 2 \% 5 = 2)$$$ then $$$Mohamed$$$ score $$$= 4 + 2 = 6.$$$

Since $$$Mohamed$$$ score $$$= 6$$$ and $$$Kero$$$ score $$$= 3$$$, then $$$Mohamed$$$ is the winner.