The Backpack

Problem Description

cc has a backpack of volume $w$ and $n$ items, each of volume $a_i$.

cc wants to put some of the items into the backpack so that their total volume is at least half of the backpack's volume but does not exceed it, that is:

Help cc decide whether there is a valid combination of items. If so, output YES; otherwise output NO. cc will take at least one item.

Input Format

The first line gives the number of test cases $T$.

For each test case:

• The first line gives $n$ and $w$: the number of items and the total volume of the backpack.
• The second line gives a sequence $a_1, \dots, a_n$, the volumes of the items.

Output Format

For each test case, output YES if a valid combination exists, otherwise NO.

Sample Input

3
1 3
3
6 2
19 8 19 69 9 4
7 12
1 1 1 17 1 1 1

Sample Output

YES
NO
YES

Constraints

$1 \le T \le 10^4$

$\sum n \le 2 \times 10^5$, $1 \le w \le 10^{18}$

$0 \le a_i \le 10^9$