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}\color{black}, 2,\color{red}{2}\color{black},\color{red}{3}\color{black}, 6] $ , $ [\color{red}{4}\color{black}, \color{red}{2}\color{black}, 2, \color{red}{3}\color{black}, 6] $ . At the same time dances $ [\color{red}{4}\color{black}, 2, 2, \color{red}{3}\color{black}, 6] $ , $ [4, \color{red}{2}\color{black}, \color{red}{2}\color{black}, \color{red}{3}\color{black}, 6] $ , $ [\color{red}{4}\color{black}, 2, 2, \color{red}{3}\color{black}, \color{red}{6}\color{black}] $ are not magnificent. In the dance $ [\color{red}{4}\color{black}, 2, 2, \color{red}{3}\color{black}, 6] $ only $ 2 $ students participate, although $ m = 3 $ . The dance $ [4, \color{red}{2}\color{black}, \color{red}{2}\color{black}, \color{red}{3}\color{black}, 6] $ involves students with levels $ 2 $ and $ 2 $ , although levels of all dancers must be pairwise distinct. In the dance $ [\color{red}{4}\color{black}, 2, 2, \color{red}{3}\color{black}, \color{red}{6}\color{black}] $ 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.

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 $ .

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 $ .

In the first testcase, Ira can set such magnificent dances: $ [\color{red}{8}\color{black}, 10, 10, \color{red}{9}\color{black}, \color{red}{6}\color{black}, 11, \color{red}{7}\color{black}] $ , $ [\color{red}{8}\color{black}, \color{red}{10}\color{black}, 10, \color{red}{9}\color{black}, 6, 11, \color{red}{7}\color{black}] $ , $ [\color{red}{8}\color{black}, 10, \color{red}{10}\color{black}, \color{red}{9}\color{black}, 6, 11, \color{red}{7}\color{black}] $ , $ [\color{red}{8}\color{black}, 10, \color{red}{10}\color{black}, \color{red}{9}\color{black}, 6, \color{red}{11}\color{black}, 7] $ , $ [\color{red}{8}\color{black}, \color{red}{10}\color{black}, 10, \color{red}{9}\color{black}, 6, \color{red}{11}\color{black}, 7] $ . The second testcase is explained in the statements.