CF1833F.Ira and Flamenco

Ira loves Spanish flamenco dance very much. She decided to start her own dance studio and found $n$ students, $i$th of whom has level $a_i$.

Ira can choose several of her students and set a dance with them. So she can set a huge number of dances, but she is only interested in magnificent dances. The dance is called magnificent if the following is true:

• exactly $m$ students participate in the dance;
• levels of all dancers are pairwise distinct;
• levels of every two dancers have an absolute difference strictly less than $m$.

For example, if $m = 3$ and $a = [4, 2, 2, 3, 6]$, the following dances are magnificent (students participating in the dance are highlighted in red): $[\color{red}{4}, 2, \color{red}{2}, \color{red}{3}, 6]$, $[\color{red}{4}, \color{red}{2}, 2, \color{red}{3}, 6]$. At the same time dances $[\color{red}{4}, 2, 2, \color{red}{3}, 6]$, $[4, \color{red}{2}, \color{red}{2}, \color{red}{3}, 6]$, $[\color{red}{4}, 2, 2, \color{red}{3}, \color{red}{6}]$ are not magnificent.

In the dance $[\color{red}{4}, 2, 2, \color{red}{3}, 6]$ only $2$ students participate, although $m = 3$.

The dance $[4, \color{red}{2}, \color{red}{2}, \color{red}{3}, 6]$ involves students with levels $2$ and $2$, although levels of all dancers must be pairwise distinct.

In the dance $[\color{red}{4}, 2, 2, \color{red}{3}, \color{red}{6}]$ students with levels $3$ and $6$ participate, but $|3 - 6| = 3$, although $m = 3$.

Help Ira count the number of magnificent dances that she can set. Since this number can be very large, count it modulo $10^9 + 7$. Two dances are considered different if the sets of students participating in them are different.

伊菈非常热爱西班牙弗拉门戈舞蹈。她决定创办自己的舞蹈工作室，并找到了 $n$ 名学生，其中第 $i$ 名学生的舞蹈水平为 $a_i$。

伊菈可以选择她的一些学生来编排一支舞蹈。因此，她可以编排出大量不同的舞蹈，但她只对“辉煌舞蹈”（magnificent dance）感兴趣。一支舞蹈被称为“辉煌舞蹈”，当且仅当满足以下全部条件：

• 恰好有 $m$ 名学生参与该舞蹈；
• 所有舞者的水平两两互不相同；
• 任意两名舞者的水平之差的绝对值严格小于 $m$。

例如，若 $m = 3$，且 $a = [4, 2, 2, 3, 6]$，则以下舞蹈是辉煌舞蹈（参与舞蹈的学生以红色高亮显示）：$[\color{red}{4}, 2, \color{red}{2}, \color{red}{3}, 6]$、$[\color{red}{4}, \color{red}{2}, 2, \color{red}{3}, 6]$。而以下舞蹈则不是辉煌舞蹈：$[\color{red}{4}, 2, 2, \color{red}{3}, 6]$、$[4, \color{red}{2}, \color{red}{2}, \color{red}{3}, 6]$、$[\color{red}{4}, 2, 2, \color{red}{3}, \color{red}{6}]$。

在舞蹈 $[\color{red}{4}, 2, 2, \color{red}{3}, 6]$ 中，仅有 $2$ 名学生参与，但要求 $m = 3$。

舞蹈 $[4, \color{red}{2}, \color{red}{2}, \color{red}{3}, 6]$ 中包含了两名水平均为 $2$ 的学生，但所有舞者水平必须两两互不相同。

舞蹈 $[\color{red}{4}, 2, 2, \color{red}{3}, \color{red}{6}]$ 中包含了水平为 $3$ 和 $6$ 的学生，但 $|3 - 6| = 3$，而要求该差值严格小于 $m = 3$。

请帮助伊菈计算她能编排的辉煌舞蹈的数量。由于该数量可能非常大，请对 $10^9 + 7$ 取模输出结果。若两支舞蹈所包含的学生集合不同，则视为不同的舞蹈。

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — number of testcases.

The first line of each testcase contains integers $n$ and $m$ ($1 \le m \le n \le 2 \cdot 10^5$) — the number of Ira students and the number of dancers in the magnificent dance.

The second line of each testcase contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$) — levels of students.

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

第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。

每个测试用例的第一行包含两个整数 $n$ 和 $m$（$1 \le m \le n \le 2 \cdot 10^5$）—— 分别表示伊菈的学生人数和盛大舞蹈中的舞者人数。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \ldots, a_n$（$1 \le a_i \le 10^9$）—— 表示各位学生的水平。

保证所有测试用例的 $n$ 值之和不超过 $2 \cdot 10^5$。

For each testcase, print a single integer — the number of magnificent dances. Since this number can be very large, print it modulo $10^9 + 7$.

对于每个测试用例，输出一个整数——壮丽舞蹈的数量。由于该数可能非常大，请对 $10^9 + 7$ 取模后输出。

In the first testcase, Ira can set such magnificent dances: $[\color{red}{8}, 10, 10, \color{red}{9}, \color{red}{6}, 11, \color{red}{7}]$, $[\color{red}{8}, \color{red}{10}, 10, \color{red}{9}, 6, 11, \color{red}{7}]$, $[\color{red}{8}, 10, \color{red}{10}, \color{red}{9}, 6, 11, \color{red}{7}]$, $[\color{red}{8}, 10, \color{red}{10}, \color{red}{9}, 6, \color{red}{11}, 7]$, $[\color{red}{8}, \color{red}{10}, 10, \color{red}{9}, 6, \color{red}{11}, 7]$.

The second testcase is explained in the statements.

在第一个测试用例中，Ira 可以设置如下精彩的舞蹈序列：$[\color{red}{8}, 10, 10, \color{red}{9}, \color{red}{6}, 11, \color{red}{7}]$、$[\color{red}{8}, \color{red}{10}, 10, \color{red}{9}, 6, 11, \color{red}{7}]$、$[\color{red}{8}, 10, \color{red}{10}, \color{red}{9}, 6, 11, \color{red}{7}]$、$[\color{red}{8}, 10, \color{red}{10}, \color{red}{9}, 6, \color{red}{11}, 7]$、$[\color{red}{8}, \color{red}{10}, 10, \color{red}{9}, 6, \color{red}{11}, 7]$。

第二个测试用例已在题目描述中说明。