Funny Game

Bob has an array \(\{a_1,a_2,\dots,a_n\}\), each element is an integer between 1 and \(n\). Bob also has \(m\) functions whose domain and codomain are both \(\{1, 2, \dots, n\}\). Bob and Alice begin to play a game on the array. Alice plays first. For each turn, the player can choose a function \(f\) and make every \(a_i\ (1 \le i \le n)\) become \(f(a_i)\). For example, the array is \(\{1, 1, 2, 4, 5\}\) and \(f(1) = 1, f(2) = 3, f(3) = 4, f(4) = 1, f(5) = 2\). Then after the operation the array will become \(\{1, 1, 3, 1, 2\}\). If all the element in the array is same, then Alice wins and the game stops. So you can see that Bob's goal is to stop Alice. Suppose that both Alice and Bob play optimally. Alice wants to know if she can always win no matter what the array looks like.

There are multiple test cases. The first line of input contains an integer \(T\ (1 \le T \le 200)\), indicating the number of test cases. For each test case: The first line contains two integers \(n\) and \(m\) (\(1 \le n, m \le 100\)), indicating the element in the array and the number of functions. In the next \(m\) lines, each contains \(n\) integers \(f(1), f(2), \dots, f(n)\) (\(1 \le f(i) \le n, 1 \le i \le n\)).

For each case, output "YES"(without quotes) if Alice can always win no matter what the array looks like, otherwise output "NO"(without quotes).

2
5 1
1 3 4 1 2
5 1
2 3 4 5 1

YES
NO

BestCoder Round #27