#11082Matrix Decompressing

Some R × C matrix of positive integers is encoded and represented by its R cumulative row sum and C column sum entries. Given, R, C and those R + C cumulative row sum and column sums, you want to decode the matrix (i.e., find all the individual R ∗ C entries).

Here,

Or in other words, the i-th row sum is the sum of all the entries in row i. And the cumulative i-th row sum is the sum of all the row sums from row 1 to row i (inclusive).

Input

There can be multiple test cases. The first line of input contains the number of test cases, T (1 ≤ T ≤ 100). Each test case contains 3 lines of input. The first line of the test case gives the size of the matrix: the number of rows, R (1 ≤ R ≤ 20) and the number of columns C (1 ≤ C ≤ 20). The next line contains all the R cumulative row sums, and the last line of the test case contains the C cumulative column sums. Any two successive numbers in the same line is separated by a single space.

Output