{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003e\n Patrick Star found the Ringland! It\u0027s marriage season in Ringland!\u003cbr\u003e\u003cbr\u003e\n Ringland has a form of a circle\u0027s boundary of length $L$.\u003cbr\u003e\u003cbr\u003e\n There are $N$ bridegrooms and $N$ brides, and bridegrooms decided to marry brides.\u003cbr\u003e\u003cbr\u003e\n Of course, each bridegroom should choose exactly one bride, and each bride should be chosen by exactly one bridegroom.\u003cbr\u003e\u003cbr\u003e\n All objects in Ringland are located on the boundary of the circle, including the capital, bridegrooms\u0027 castles and brides\u0027 palaces. The castle of the i-th bridegroom is located at the distance $a_i$ from the capital in clockwise direction, and the palace of the i-th bride is located at the distance $b_i$ from the capital in clockwise direction.\u003cbr\u003e\u003cbr\u003e\n Let\u0027s define the inconvenience of a marriage the summary distance of every bride should walk along the circle from her palace to her bridegroom\u0027s castle in the shortest direction (in clockwise or counter-clockwise direction).\u003cbr\u003e\u003cbr\u003e\n Help Patrick Star to calculate the smallest inconvenience among all marriages !\n\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line contain a integer $T$ (no morn than 10), the following is $T$ test case, for each test case :\u003cbr\u003e\u003cbr\u003e\nThe first line contains two integers $N$ and $L$ ($1 \\le N \\le 5 * 10^5, 1\\le L \\le 10^9$) --- the number of bridegrooms and brides and the length of Ringland.\u003cbr\u003e\u003cbr\u003e\nThe next line contains $N$ integers, $a_1, a_2, ..., a_n$ ($0 \\le a_1 \\le a_2 \\le ... \\le a_n \u0026lt; L$) --- the distances from the capital to the castles of bridegrooms in clockwise direction.\u003cbr\u003e\u003cbr\u003e\nThe next line contains $N$ integers, $b_1, b_2, ..., b_n$ ($0 \\le b_1 \\le b_2 \\le ... \\le b_n \u0026lt; L$) --- the distances from the capital to the palaces of brides in clockwise direction.\u003cbr\u003e\u003cbr\u003e\nAttention: you may need fast read function."}},{"title":"Output","value":{"format":"HTML","content":"For each test case print one line,\u003cbr\u003e\u003cbr\u003e\nThis line contain only one integer, the smallest possible inconvenience of the wedding."}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e\u003cpre\u003e1\r\n2 5\r\n3 4\r\n0 2\u003c/pre\u003e\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e\u003cpre\u003e2\u003c/pre\u003e\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}