A. Color the Picturetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA 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?InputEach 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.OutputFor each test case, print "Yes" (without quotes) if it is possible to color a beautiful picture. Otherwise, print "No" (without quotes).ExampleInput
64 6 312 9 83 3 28 83 3 29 54 5 210 115 4 29 1110 10 311 45 14Output
Yes
No
Yes
Yes
No
No
NoteIn the first test case, one possible solution is as follows:  In the third test case, we can color all cells with pigment 1.
64 6 312 9 83 3 28 83 3 29 54 5 210 115 4 29 1110 10 311 45 14
Yes No Yes Yes No No 
['constructive algorithms', 'greedy', 'math', '*1500']