There are m students in a classroom, out of which n of them are girls. The teacher, Mr X wants to arrange all the students in a line. X thinks that his class girls are very talkative. So he doesn't want any two girls to be together. Mr X wants to know the number of ways he can arrange these m students. Help him out.
The first line contains a single integer t (1≤t≤105), denoting the number of testcases. Each of the next t lines contain two integers m and n (1<n≤m≤106).
For each test case print the answer modulo 109+7 in a single line.