CF1798F Gifts from Grandfather Ahmed

Grandfather Ahmed's School has $ n+1 $ students. The students are divided into $ k $ classes, and $ s_i $ students study in the $ i $ -th class. So, $ s_1 + s_2 + \ldots + s_k = n+1 $ . Due to the upcoming April Fools' Day, all students will receive gifts! Grandfather Ahmed planned to order $ n+1 $ boxes of gifts. Each box can contain one or more gifts. He plans to distribute the boxes between classes so that the following conditions are satisfied: 1. Class number $ i $ receives exactly $ s_i $ boxes (so that each student can open exactly one box). 2. The total number of gifts in the boxes received by the $ i $ -th class should be a multiple of $ s_i $ (it should be possible to equally distribute the gifts among the $ s_i $ students of this class). Unfortunately, Grandfather Ahmed ordered only $ n $ boxes with gifts, the $ i $ -th of which contains $ a_i $ gifts. Ahmed has to buy the missing gift box, and the number of gifts in the box should be an integer between $ 1 $ and $ 10^6 $ . Help Ahmed to determine, how many gifts should the missing box contain, and build a suitable distribution of boxes to classes, or report that this is impossible.

The first line of the input contains two integers $ n $ and $ k $ ( $ 1 \le n, k \le 200 $ , $ k \le n + 1 $ ). The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 10^6 $ ) — the number of gifts in the available boxes. The third line contains $ k $ integers $ s_1, s_2, \ldots, s_k $ ( $ 1 \le s_i \le n+1 $ ) — the number of students in classes. It is guaranteed that $ \sum s_i = n+1 $ .

If there is no way to buy the remaining box, output the integer $ -1 $ in a single line. Otherwise, in the first line, output a single integer $ s $ — the number of gifts in the box that Grandfather Ahmed should buy ( $ 1 \le s \le 10^6 $ ). Next, in $ k $ lines, print the distribution of boxes to classes. In the $ i $ -th line print $ s_i $ integers — the sizes of the boxes that should be sent to the $ i $ -th class. If there are multiple solutions, print any of them.

In the first test, Grandfather Ahmed can buy a box with just $ 1 $ gift. After that, two boxes with $ 7 $ gifts are sent to the first class. $ 7 + 7 = 14 $ is divisible by $ 2 $ . And the second class gets boxes with $ 1, 7, 127 $ gifts. $ 1 + 7 + 127 = 135 $ is evenly divisible by $ 3 $ . In the second test, the classes have sizes $ 6 $ , $ 1 $ , $ 9 $ , and $ 3 $ . We show that the available boxes are enough to distribute into classes with sizes $ 6 $ , $ 9 $ , $ 3 $ , and in the class with size $ 1 $ , you can buy a box of any size. In class with size $ 6 $ we send boxes with sizes $ 7 $ , $ 1 $ , $ 7 $ , $ 6 $ , $ 5 $ , $ 4 $ . $ 7 + 1 + 7 + 6 + 5 + 4 = 30 $ is divisible by $ 6 $ . In class with size $ 9 $ we send boxes with sizes $ 1 $ , $ 2 $ , $ 3 $ , $ 8 $ , $ 3 $ , $ 2 $ , $ 9 $ , $ 8 $ , $ 9 $ . $ 1 + 2 + 3 + 8 + 3 + 2 + 9 + 8 + 9 = 45 $ is divisible by $ 9 $ . The remaining boxes ( $ 6 $ , $ 5 $ , $ 4 $ ) are sent to the class with size $ 3 $ . $ 6 + 5 + 4 = 15 $ is divisible by $ 3 $ .