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?

一幅图像可以表示为一个 $n\times m$ 的网格（$n$ 行、$m$ 列），其中 $n \cdot m$ 个单元格中的每一个均被染成一种颜色。你有 $k$ 种不同颜色的颜料，且每种颜料的数量有限：具体而言，第 $i$ 种颜料最多可给 $a_i$ 个单元格上色。

若图像中每个单元格都至少有 $3$ 个环面邻接单元格（toroidal neighbor）与其颜色相同，则该图像被称为“优美的”。

两个单元格被称为环面邻接单元格，当且仅当它们在环面上共享一条边。换言之，对任意整数 $1 \leq x_1,x_2 \leq n$ 和 $1 \leq y_1,y_2 \leq m$，位于第 $x_1$ 行、第 $y_1$ 列的单元格与位于第 $x_2$ 行、第 $y_2$ 列的单元格互为环面邻接单元格，当且仅当满足以下两个条件之一：

• $x_1-x_2 \equiv \pm1 \pmod{n}$ 且 $y_1=y_2$，或
• $y_1-y_2 \equiv \pm1 \pmod{m}$ 且 $x_1=x_2$。

注意：每个单元格恰好有 $4$ 个环面邻接单元格。例如，当 $n=3$ 且 $m=4$ 时，单元格 $(1, 2)$（即第 $1$ 行、第 $2$ 列的单元格）的环面邻接单元格为：$(3, 2)$、$(2, 2)$、$(1, 3)$、$(1, 1)$。如下图中灰色单元格所示：

灰色单元格表示 $(1, 2)$ 的环面邻接单元格。

能否使用所给颜料为所有单元格上色，从而构造出一幅优美的图像？

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 $10^5$.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \leq t \leq 10^4$）。随后是各测试用例的描述。

每个测试用例的第一行包含三个整数 $n$、$m$ 和 $k$（$3 \leq n,m \leq 10^9$，$1 \leq k \leq 10^5$）——分别表示图片的行数、列数以及颜料种类数。

下一行包含 $k$ 个整数 $a_1,a_2,\dots, a_k$（$1 \leq a_i \leq 10^9$）——其中 $a_i$ 表示第 $i$ 种颜料最多可涂色的格子数。

保证所有测试用例中 $k$ 的总和不超过 $10^5$。

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

对于每个测试用例，如果能够绘制出一幅美丽的图画，则输出“Yes”（不带引号）；否则，输出“No”（不带引号）。

In the first test case, one possible solution is as follows:

In the third test case, we can color all cells with pigment $1$.

在第一个测试用例中，一种可能的解法如下：

在第三个测试用例中，我们可以用颜料 $1$ 给所有格子染色。