Problem: A binary matrix is an m x n matrix consisting of only zeroes and ones. Now you are given m integers, ith integer indicating the summation of the values of cells in ith row. You are also given n integers, ith integer indicating the summation of the values of cells in jth column.
Your task is to generate the binary matrix. As there can be multiple solutions, we want the solution which is lexicographically smallest. To compare two solutions, we first find the cell (topmost, then leftmost) where the solutions differ; then the solution which contains 0 in that cell is lexicographically smaller. So,
001 001
010 < 100
100 010
Input.
Input starts with an integer T (≤ 125), denoting the number of test cases.
Each case starts with a line containing two integers: m and n (1 ≤ m, n ≤ 50). The next line contains m integers, separated by a single space, denoting the row sums. The next line contains n integers, separated by spaces, denoting the column sum. All the integers will be between 0 and 50 (inclusive).
Output.
For each case, print the case number first. Then if there is no solution, then print 'impossible' on the same line. Otherwise, from the next line, print m lines each having n characters denoting the binary matrix as stated above.
Sample Input
5
3 3
1 1 1
1 1 1
3 3
1 1 2
2 2 1
2 3
30 30
30 20 10
2 9
5 5
1 1 2 1 1 1 1 1 1
3 3
1 2 3
3 2 1
Output for Sample Input
Case 1:
001
010
100
Case 2: impossible
Case 3: impossible
Case 4:
001001111
111110000
Case 5:
100
110
111
/***/ Please give some Hint or pseudocode [if needed] /***/
