There is a hidden sequence (a_1,a_2,\ldots,a_n) of (n) integers ((n \ge 2)). It is guaranteed that (|a_i| \le 1000) for all (1 \le i \le n). Let's define a function (f(x)) as follows: ()f(x)=\sum_{i=1}^n a_i \cdot |i-x|() Given (n) values (f(1),f(2),\ldots,f(n)), please determine the values of (a_1,a_2,\ldots,a_n). It is guaranteed that the values (a_1,a_2,\ldots,a_n) can be determined uniquely. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains a single integer (n) ((\color{red}{2} \le n \le 300\,000)). The second line of each test case contains (n) integers (f(1),f(2),\ldots,f(n)) ((-10^{14} \le f(i) \le 10^{14})). It is guaranteed that the sum of (n) over all test cases does not exceed (300\,000). For each test case, output (n) integers (a_1,a_2,\ldots,a_n) on a separate line ((|a_i| \le 1000)). It is guaranteed that the values (a_1,a_2,\ldots,a_n) can be determined uniquely. In the first test case, the hidden sequence is (a=1,4,2,3). The values (f(1),f(2),\ldots,f(n)) are as follows: (f(1) = 1 \cdot |1-1| + 4 \cdot |2-1| + 2 \cdot |3-1| + 3 \cdot |4-1| = 0+4+4+9 = 17); (f(2) = 1 \cdot |1-2| + 4 \cdot |2-2| + 2 \cdot |3-2| + 3 \cdot |4-2| = 1+0+2+6 = 9); (f(3) = 1 \cdot |1-3| + 4 \cdot |2-3| + 2 \cdot |3-3| + 3 \cdot |4-3| = 2+4+0+3 = 9); (f(4) = 1 \cdot |1-4| + 4 \cdot |2-4| + 2 \cdot |3-4| + 3 \cdot |4-4| = 3+8+2+0 = 13).