Score : 600 points
Snuke has a blackboard and a set S consisting of N integers. The i-th element in S is S_i.
He wrote an integer X on the blackboard, then performed the following operation N times:
There are N! possible orders in which the elements are removed from S. For each of them, find the number that would be written on the blackboard after the N operations, and compute the sum of all those N! numbers modulo 10^{9}+7.
Input is given from Standard Input in the following format:
N X S_1 S_2 \ldots S_{N}
Print the answer.
2 19 3 7
3
5 82 22 11 6 5 13
288
10 100000 50000 50001 50002 50003 50004 50005 50006 50007 50008 50009
279669259