F. Gifts from Grandfather Ahmedtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputGrandfather 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:  Class number i receives exactly s_i boxes (so that each student can open exactly one box).  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.InputThe 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.OutputIf 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.ExamplesInput
4 2
7 7 7 127
2 3
Output
1
7 7 
7 127 1 
Input
18 4
1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
6 1 9 3
Output
9
7 1 7 6 5 4 
9 
1 2 3 8 3 2 9 8 9 
6 5 4 
NoteIn 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.
4 2
7 7 7 127
2 3

1 7 7  7 127 1  
['dp', 'math', 'number theory', '*2500']