B"Mircea has n pictures. The i -th picture is a square with a side length of s_i centimeters. He mounted each picture on a square piece of cardboard so that each picture has a border of w centimeters of cardboard on all sides. In total, he used c square centimeters of cardboard. Given the picture sizes and the value c , can you find the value of w ? Please note that the piece of cardboard goes behind each picture, not just the border. The first line contains a single integer t ( 1 <= q t <= q 1000 ) -- the number of test cases. The first line of each test case contains two positive integers n ( 1 <= q n <= q 2 cdot 10^5 ) and c ( 1 <= q c <= q 10^{18} ) -- the number of paintings, and the amount of used square centimeters of cardboard. The second line of each test case contains n space-separated integers s_i ( 1 <= q s_i <= q 10^4 ) -- the sizes of the paintings. The sum of n over all test cases doesn't exceed 2 cdot 10^5 . Additional constraint on the input: Such an integer w exists for each test case. Please note, that some of the input for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language (like long long for C++). For each test case, output a single integer -- the value of w ( w geq 1 ) which was used to use exactly c squared centimeters of cardboard. The first test case is explained in the statement. For the second test case, the chosen w was 2 , thus the only cardboard covers an area of c = (2 cdot 2 + 6)^2 = 10^2 = 100 squared centimeters. For the third test case, the chosen w was 4 , which obtains the covered area c = (2 cdot 4 + 2)^2 x 5 = 10^2 x 5 = 100 x 5 = 500 squared centimeters. "...