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

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$ 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.