B"You're given a multiset of non-negative integers {a_1, a_2, ... , a_n } . In one step you take two elements x and y of the multiset, remove them and insert their mean value frac{x + y}{2} back into the multiset. You repeat the step described above until you are left with only two numbers A and B . What is the maximum possible value of their absolute difference |A-B| ? Since the answer is not an integer number, output it modulo 10^9+7 . Each test contains multiple test cases. The first line contains the number of test cases t ( 1 <= t <= 100 ). Description of the test cases follows. The first line of each test case contains a single integer n ( 2 <= n <= 10^6 ) -- the size of the multiset. The second line contains n integers a_1, a_2, ldots, a_n ( 0 <= a_i <= 10^9 ) -- the elements of the multiset. It is guaranteed that the sum of n over all test cases does not exceed 10^6 . For each test case, output a single integer, the answer to the problem modulo 10^9+7 . Formally, let M = 10^9+7 . It can be shown that the answer can be expressed as an irreducible fraction frac{p}{q} , where p and q are integers and q not equiv 0 pmod{M} . Output the integer equal to p cdot q^{-1} bmod M . In other words, output an integer x such that 0 <= x < M and x cdot q equiv p pmod{M} . In the first case, you can't do any operations, so the answer is |7-3|=4 . In the second case, one of the optimal sequence of operations: In the third case, the exact answer is frac{3}{2} , and 500 ,000 ,005 cdot 2 equiv 3 pmod{10^9+7} . "...