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

Class Photo Groups - Repovive Career Starter Round 2 | Repovive | Repovive

10B. Class Photo Groups

1000 pts1s256 MB

A school wants to split $n$ students into two photo groups.

The height of the $i$ -th student is $a_i$ .

The two groups must be non-empty. A group is called good if the difference between the tallest and the shortest student in that group is at most $d$ .

Determine whether it is possible to split all students into two good groups.

Constraints

$2 \le n \le 1000$
$0 \le d \le 10^6$
$1 \le a_i \le 10^6$

Input

n \quad d

a_1 \quad a_2 \quad \cdots \quad a_n

Output

Print Yes if it is possible to split the students into two good groups.

Otherwise, print No.

Samples

Input

5 3
150 153 160 162 161

Explanation

One possible split is to put the students with heights $150$ and $153$ in one group, and the students with heights $160$ , $161$ , and $162$ in the other group.

Both groups are good.

Output

Yes

Input

5 3
150 154 160 161 162

Explanation

The students with heights $160$ , $161$ , and $162$ can form a good group.

However, the remaining heights $150$ and $154$ differ by more than $d$ .

No split makes both groups good.

Output

No

Input

4 0
170 180 170 180

Explanation

One group can contain the two students with height $170$ , and the other group can contain the two students with height $180$ .

In both groups, the tallest and shortest students have the same height, so the difference is $0$ .

Output

Yes

A school wants to split $n$ students into two photo groups.

The height of the $i$ -th student is $a_i$ .

The two groups must be non-empty. A group is called good if the difference between the tallest and the shortest student in that group is at most $d$ .

Determine whether it is possible to split all students into two good groups.

$2 \le n \le 1000$
$0 \le d \le 10^6$
$1 \le a_i \le 10^6$

n \quad d

a_1 \quad a_2 \quad \cdots \quad a_n

One possible split is to put the students with heights $150$ and $153$ in one group, and the students with heights $160$ , $161$ , and $162$ in the other group.

Both groups are good.

The students with heights $160$ , $161$ , and $162$ can form a good group.

However, the remaining heights $150$ and $154$ differ by more than $d$ .

No split makes both groups good.

One group can contain the two students with height $170$ , and the other group can contain the two students with height $180$ .

In both groups, the tallest and shortest students have the same height, so the difference is $0$ .