CF1710A Color the Picture

A picture can be represented as an $ n\times m $ grid ( $ n $ rows and $ m $ columns) so that each of the $ n \cdot m $ cells is colored with one color. You have $ k $ pigments of different colors. You have a limited amount of each pigment, more precisely you can color at most $ a_i $ cells with the $ i $ -th pigment. A picture is considered beautiful if each cell has at least $ 3 $ toroidal neighbors with the same color as itself. Two cells are considered toroidal neighbors if they toroidally share an edge. In other words, for some integers $ 1 \leq x_1,x_2 \leq n $ and $ 1 \leq y_1,y_2 \leq m $ , the cell in the $ x_1 $ -th row and $ y_1 $ -th column is a toroidal neighbor of the cell in the $ x_2 $ -th row and $ y_2 $ -th column if one of following two conditions holds: - $ x_1-x_2 \equiv \pm1 \pmod{n} $ and $ y_1=y_2 $ , or - $ y_1-y_2 \equiv \pm1 \pmod{m} $ and $ x_1=x_2 $ . Notice that each cell has exactly $ 4 $ toroidal neighbors. For example, if $ n=3 $ and $ m=4 $ , the toroidal neighbors of the cell $ (1, 2) $ (the cell on the first row and second column) are: $ (3, 2) $ , $ (2, 2) $ , $ (1, 3) $ , $ (1, 1) $ . They are shown in gray on the image below: The gray cells show toroidal neighbors of $ (1, 2) $ .Is it possible to color all cells with the pigments provided and create a beautiful picture?

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \leq t \leq 10^4 $ ). The description of the test cases follows. The first line of each test case contains three integers $ n $ , $ m $ , and $ k $ ( $ 3 \leq n,m \leq 10^9 $ , $ 1 \leq k \leq 10^5 $ ) — the number of rows and columns of the picture and the number of pigments. The next line contains $ k $ integers $ a_1,a_2,\dots, a_k $ ( $ 1 \leq a_i \leq 10^9 $ ) — $ a_i $ is the maximum number of cells that can be colored with the $ i $ -th pigment. It is guaranteed that the sum of $ k $ over all test cases does not exceed $ 10^5 $ .

For each test case, print "Yes" (without quotes) if it is possible to color a beautiful picture. Otherwise, print "No" (without quotes).

In the first test case, one possible solution is as follows: In the third test case, we can color all cells with pigment $ 1 $ .