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.

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 $ .

For each test case, if it is possible to turn $ a $ into $ [1] $ , print "YES", otherwise print "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] $ .