Description

deepl翻译

多雷米生活在一个由 $n$ 个城市组成的国家，这些城市的编号从 $1$ 到 $n$ ，其中 $a_i$ 个人生活在 $i$ 个城市中。它可以被建模为一个无向图，其中有 $n$ 个节点。

最初，图中没有边。现在，多雷米想让这个图连接起来。

为此，她可以在 $i$ 和 $j$ 之间添加一条边，如果

$\sum _ {k \in S} a_k \ge i\cdot j \cdot c$

其中 $S$ 是当前位于 $i$ 或 $j$ 的同一相连组件中的所有节点的集合，而 $c$ 是给定的常数。

多雷米能否使图形连通？

如果存在从 $i$ 到 $j$ 的路径，则两个节点 $(i, j)$ 位于同一个连通部分。如果一个图的所有节点都在同一个连通部分中，那么这个图就是连通的。

Input

The input consists of multiple test cases. The first line contains a single integer $t$ ($1\le t\le 10^4$) — the number of test cases. The description of the test cases follows.

The first line contains two integers $n$, $c$ ($2\le n\le 2\cdot 10^5$, $1 \le c \le 10^6$) — the number of nodes and the constant.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($0 \le a_i \le 10^{12}$) — the number of people living in the $i$-th city.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$.

Output

For each test case, print "YES" (without quotes), if it is possible to make the graph connected, and "NO" (without quotes) otherwise.

You can print letters in any case (upper or lower).

7
4 10
0 20 15 10
2 1
1 1
5 1
0 1 0 4 199
5 2
1 1 3 1 1
5 5
5 6 1 10 2
5 1000000
1000000000000 1000000000000 1000000000000 1000000000000 1000000000000
3 1
0 0 2
 
 
 
 
 
 
 
 

Yes
Yes
Yes
No
No
Yes
No

Note

In the first test case, Doremy can add edges in the following order:

1. Add $(1,2)$. This operation is valid because $a_1 + a_2 = 20 \ge i\cdot j \cdot c = 20$.
2. Add $(1,3)$. This operation is valid because $a_1 + a_2 + a_3 = 35 \ge i \cdot j \cdot c = 30$.
3. Add $(1,4)$. This operation is valid because $a_1 + a_2 + a_3 + a_4 = 45 \ge i \cdot j \cdot c = 40$.

In the second test case, Doremy can add edge $(1,2)$ because $a_1 + a_2 =2 \ge 1 \cdot 2 \cdot 1$. After that, the graph is connected.

In the third test case, Doremy can add edges in the order $(5,4)$, $(5,3)$, $(5,2)$ and $(5,1)$.

In the fourth test case, Doremy cannot add any edge at all.