16 NHL teams in the first playoff round divided in pairs and to play series until 4 wins (thus the series could finish with score 4-0, 4-1, 4-2, or 4-3). After that 8 winners of the series play the second playoff round divided into 4 pairs to play series until 4 wins, and so on. After all the final round is over, it happens that $k$ teams have non-negative balance of wins (for example, the team that won in the first round with a score of 4-2 and lost in the second with a score of 4-3 fits the condition: it has $4+3=7$ wins and $2+4=6$ losses). Find the least possible $k$.
1. **Understanding the Problem:**
   - There are 16 teams in the first playoff round.
   - Each series is played until one team wins 4 games.
   - The series can end with scores of 4-0, 4-1, 4-2, or 4-3.
   - After each round, the winners advance to the next round.
   - We need to find the least possible number of teams, \( k \), that have a non-negative balance of wins after the final round.

2. **Analyzing the Rounds:**
   - **First Round:**
     - 16 teams play, resulting in 8 winners and 8 losers.
     - Each winner has at least 4 wins.
     - Each loser has at most 3 wins.
   - **Second Round:**
     - 8 winners from the first round play, resulting in 4 winners and 4 losers.
     - Each winner has at least 4 more wins, totaling at least 8 wins.
     - Each loser has at least 4 wins from the first round and at most 3 wins in the second round, totaling at most 7 wins.
   - **Third Round:**
     - 4 winners from the second round play, resulting in 2 winners and 2 losers.
     - Each winner has at least 4 more wins, totaling at least 12 wins.
     - Each loser has at least 8 wins from the first two rounds and at most 3 wins in the third round, totaling at most 11 wins.
   - **Final Round:**
     - 2 winners from the third round play, resulting in 1 winner and 1 loser.
     - The winner has at least 4 more wins, totaling at least 16 wins.
     - The loser has at least 12 wins from the first three rounds and at most 3 wins in the final round, totaling at most 15 wins.

3. **Calculating the Balance of Wins:**
   - A team has a non-negative balance of wins if the number of wins is greater than or equal to the number of losses.
   - Each team plays a maximum of 4 rounds, and in each round, they can lose at most 3 games.
   - Therefore, the maximum number of losses for any team is \( 3 \times 4 = 12 \).

4. **Finding the Least Possible \( k \):**
   - The winner of the final round has at least 16 wins and at most 12 losses, so they have a non-negative balance.
   - The loser of the final round has at least 15 wins and at most 12 losses, so they also have a non-negative balance.
   - The losers of the third round have at most 11 wins and at least 12 losses, so they have a negative balance.
   - The losers of the second round have at most 7 wins and at least 6 losses, so they have a negative balance.
   - The losers of the first round have at most 3 wins and at least 4 losses, so they have a negative balance.

Therefore, the least possible number of teams with a non-negative balance of wins is 2.

The final answer is \( \boxed{ k = 2 } \).