#####   ######  #####    ###    #   #  ###  #   #  ######
##  ##  ##      ##  ##  ## ##   #   #   #   #   #  ##
#####   ####    #####   #   #   #   #   #   #   #  ####
##  #   ##      ##      ## ##    # #    #    # #   ##
##   #  ######  ##       ###      #    ###    #    ######

$ curl repovive.com/contests/10/problems/D

░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░██████████████████████████████████████████

Ice Cream - Repovive Career Starter Round 2 | Repovive | Repovive

10D. Ice Cream

2000 pts1s256 MB

Hannah has $n$ ice creams. The $i$ -th ice cream has initial volume $v_i$ .

Each second, the following steps happen in order:

If all ice creams have volume $0$ , Hannah wins immediately.
Otherwise, if any ice cream has volume $0$ , Hannah loses.
All ice creams melt, so each ice cream loses $1$ unit of volume.
If every ice cream now has volume strictly less than $k$ , Hannah loses.
Hannah picks exactly one ice cream with volume at least $k$ and licks it, reducing its volume by exactly $k$ .

Determine whether Hannah can finish all the ice creams without losing.

Constraints

$1 \le n \le 2 \cdot 10^5$
$1 \le k \le 10^9$
$1 \le v_i \le 10^9$

Input

n \quad k

v_1 \quad v_2 \quad \ldots \quad v_n

Output

Print Yes if Hannah can finish all the ice creams without losing.

Otherwise, print No.

Samples

Input

2 2
4 4

Explanation

After the first melting step, the volumes become $3$ and $3$ . Hannah licks the first ice cream, so the volumes become $1$ and $3$ .

After the second melting step, the volumes become $0$ and $2$ . Hannah licks the second ice cream, so both volumes become $0$ .

At the start of the next second, all ice creams have volume $0$ , so Hannah wins.

Output

Yes

Input

1 1
1

Explanation

After the first melting step, the only ice cream has volume $0$ .

Now every ice cream has volume strictly less than $k$ , so Hannah loses before she can win.

Output

No

Input

3 2
2 4 4

Explanation

After the first melting step, the volumes become $1$ , $3$ , and $3$ . Hannah licks one of the ice creams with volume $3$ .

After the second melting step, the volumes can become $0$ , $0$ , and $2$ . Hannah licks the last ice cream with volume $2$ , so all volumes become $0$ .

At the start of the next second, Hannah wins.

Output

Yes

Hannah has $n$ ice creams. The $i$ -th ice cream has initial volume $v_i$ .

Each second, the following steps happen in order:

If all ice creams have volume $0$ , Hannah wins immediately.
Otherwise, if any ice cream has volume $0$ , Hannah loses.
All ice creams melt, so each ice cream loses $1$ unit of volume.
If every ice cream now has volume strictly less than $k$ , Hannah loses.
Hannah picks exactly one ice cream with volume at least $k$ and licks it, reducing its volume by exactly $k$ .

Determine whether Hannah can finish all the ice creams without losing.

$1 \le n \le 2 \cdot 10^5$
$1 \le k \le 10^9$
$1 \le v_i \le 10^9$

n \quad k

v_1 \quad v_2 \quad \ldots \quad v_n

After the first melting step, the volumes become $3$ and $3$ . Hannah licks the first ice cream, so the volumes become $1$ and $3$ .

After the second melting step, the volumes become $0$ and $2$ . Hannah licks the second ice cream, so both volumes become $0$ .

At the start of the next second, all ice creams have volume $0$ , so Hannah wins.

After the first melting step, the only ice cream has volume $0$ .

Now every ice cream has volume strictly less than $k$ , so Hannah loses before she can win.

After the first melting step, the volumes become $1$ , $3$ , and $3$ . Hannah licks one of the ice creams with volume $3$ .

After the second melting step, the volumes can become $0$ , $0$ , and $2$ . Hannah licks the last ice cream with volume $2$ , so all volumes become $0$ .

At the start of the next second, Hannah wins.

	#	Title	Points	Solved	Admin

	#	Title	Points	Solved	Admin

	#	Title	Points	Solved	Admin

	#	Title	Points	Solved	Admin

Commentary

My submissions

Sponsors

Ranking

Commentary

My submissions

Sponsors

Ranking

Commentary

My submissions

Sponsors

Ranking

Commentary

My submissions

Sponsors

Ranking

10D. Ice Cream

Constraints

Input

Output

Samples

10D. Ice Cream

Constraints

Input

Output

Samples