CF1746A.Maxmina

You have an array $a$ of size $n$ consisting only of zeroes and ones and an integer $k$. In one operation you can do one of the following:

• Select $2$ consecutive elements of $a$ and replace them with their minimum (that is, let $a := [a_{1}, a_{2}, \ldots, a_{i-1}, \min(a_{i}, a_{i+1}), a_{i+2}, \ldots, a_{n}]$ for some $1 \le i \le n-1$). This operation decreases the size of $a$ by $1$.
• Select $k$ consecutive elements of $a$ and replace them with their maximum (that is, let $a := [a_{1}, a_{2}, \ldots, a_{i-1}, \max(a_{i}, a_{i+1}, \ldots, a_{i+k-1}), a_{i+k}, \ldots, a_{n}]$ for some $1 \le i \le n-k+1$). This operation decreases the size of $a$ by $k-1$.

Determine if it's possible to turn $a$ into $[1]$ after several (possibly zero) operations.

你有一个长度为 $n$ 的数组 $a$，其中仅包含 $0$ 和 $1$，以及一个整数 $k$。在一次操作中，你可以执行以下两种操作之一：

• 选取 $a$ 中两个相邻的元素，并将其替换为它们的最小值（即，对某个满足 $1 \le i \le n-1$ 的下标 $i$，令 $a := [a_{1}, a_{2}, \ldots, a_{i-1}, \min(a_{i}, a_{i+1}), a_{i+2}, \ldots, a_{n}]$）。该操作使数组 $a$ 的长度减少 $1$。
• 选取 $a$ 中 $k$ 个相邻的元素，并将其替换为它们的最大值（即，对某个满足 $1 \le i \le n-k+1$ 的下标 $i$，令 $a := [a_{1}, a_{2}, \ldots, a_{i-1}, \max(a_{i}, a_{i+1}, \ldots, a_{i+k-1}), a_{i+k}, \ldots, a_{n}]$）。该操作使数组 $a$ 的长度减少 $k-1$。

判断是否可以通过若干次（可以为零次）上述操作，将 $a$ 变为 $[1]$。

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1000$). The description of the test cases follows.

The first line of each test case contains two integers $n$ and $k$ ($2 \le k \le n \le 50$), the size of array $a$ and the length of segments that you can perform second type operation on.

The second line contains $n$ integers $a_{1}, a_{2}, \ldots, a_{n}$ ($a_i$ is $0$ or $1$), elements of array $a$.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 1000$）。随后是各测试用例的描述。

每个测试用例的第一行包含两个整数 $n$ 和 $k$（$2 \le k \le n \le 50$），分别表示数组 $a$ 的大小以及可对之执行第二种操作的区间的长度。

第二行包含 $n$ 个整数 $a_{1}, a_{2}, \ldots, a_{n}$（每个 $a_i$ 为 $0$ 或 $1$），即数组 $a$ 的元素。

For each test case, if it is possible to turn $a$ into $[1]$, print "YES", otherwise print "NO".

对于每个测试用例，如果可以将 $a$ 变为 $[1]$，则输出 "YES"；否则输出 "NO"。

In the first test case, you can perform the second type operation on second and third elements so $a$ becomes $[0, 1]$, then you can perform the second type operation on first and second elements, so $a$ turns to $[1]$.

In the fourth test case, it's obvious to see that you can't make any $1$, no matter what you do.

In the fifth test case, you can first perform a type 2 operation on the first three elements so that $a$ becomes $[1, 0, 0, 1]$, then perform a type 2 operation on the elements in positions two through four, so that $a$ becomes $[1, 1]$, and finally perform the first type operation on the remaining elements, so that $a$ becomes $[1]$.

在第一个测试用例中，你可以对第二个和第三个元素执行第二种类型的操作，使 $a$ 变为 $[0, 1]$；然后对第一个和第二个元素执行第二种类型的操作，使 $a$ 变为 $[1]$。

在第四个测试用例中，显然无论你如何操作，都无法得到任何 $1$。

在第五个测试用例中，你可以首先对前三个元素执行一次类型 2 的操作，使 $a$ 变为 $[1, 0, 0, 1]$；接着对位置二至四的元素执行一次类型 2 的操作，使 $a$ 变为 $[1, 1]$；最后对剩余的元素执行一次类型 1 的操作，使 $a$ 变为 $[1]$。