Tournament

There are two very different cases hiding here. The problem looks like a tournament simulation, but simulating it would be pointless. The choices are flexible, and we only need to know whether some sequence can keep player $j$ alive.

Key observation

A player is eliminated only if they are chosen for a match.

So if we can avoid choosing player $j$ until the tournament stops, then player $j$ survives. Simple. Kinda stupid, but in the best Codeforces way.

Case 1: $k > 1$

We need player $j$ to be among the last $k$ remaining players, not necessarily the winner.

So we can try this strategy:

• never choose player $j$,
• keep making matches only between the other players,
• stop once exactly $k$ players remain.

Initially there are $n-1$ players other than $j$.

We need to eliminate exactly $n-k$ players total. Since $k > 1$, we have:

$n-k \le n-2$

So we do not need to eliminate all other players. At least one non-$j$ player can remain with player $j$ at the end.

Also, whenever the tournament still needs another elimination, there are more than $k$ players remaining. Since player $j$ is still present, the number of other players is more than $k-1$. Because $k>1$, that means there are at least two other players available to fight.

Therefore, for $k>1$, player $j$ can always survive. Strengths do not matter at all. The whole array is basically decorative furniture.

So:

$k > 1 \Rightarrow \text{YES}$

Case 2: $k=1$

Now player $j$ must be the final remaining player. They cannot just hide in a corner until the end, because everyone else must eventually be eliminated.

If some player has strength strictly greater than $a_j$, then that stronger player cannot be eliminated by player $j$. Even worse, the strongest player overall can never be eliminated by someone weaker. To make player $j$ the winner, every stronger player would need to disappear somehow, but nobody weaker can eliminate them.

So if there exists some $a_i > a_j$, player $j$ cannot win.

On the other hand, if $a_j$ is equal to the maximum strength in the array, then player $j$ can win. Any weaker player loses to them, and players with equal strength can be eliminated randomly. Since the question asks whether there is any way, ties can go in player $j$'s favor.

So for $k=1$:

$\text{YES iff } a_j = \max(a_1,a_2,\dots,a_n)$

Algorithm

For each test case:

1. Read $n,j,k$ and the array.
2. Let $x=a_j$.
3. If $k>1$, print YES.
4. Otherwise, print YES iff $x$ is the maximum array value.

Complexity

Each test case takes $O(n)$ time to read and find the maximum.

Total complexity is:

$O\left(\sum n\right)$

which easily fits the limits.