A. Artwork

**Definitions** Let $ a_1, a_2 \in \mathbb{Z}^+ $ be the number of players in team 1 and team 2, respectively. Let $ k_1, k_2 \in \mathbb{Z}^+ $ be the red card thresholds for team 1 and team 2, respectively. Let $ n \in \mathbb{Z}^+ $ be the total number of yellow cards distributed, with $ 1 \le n \le a_1 k_1 + a_2 k_2 $. Let $ x_i \in \mathbb{Z}_{\ge 0} $ be the number of yellow cards received by the $ i $-th player in team 1 ($ i = 1, \dots, a_1 $). Let $ y_j \in \mathbb{Z}_{\ge 0} $ be the number of yellow cards received by the $ j $-th player in team 2 ($ j = 1, \dots, a_2 $). **Constraints** 1. $ \sum_{i=1}^{a_1} x_i + \sum_{j=1}^{a_2} y_j = n $ 2. $ 0 \le x_i \le k_1 $ for all $ i \in \{1, \dots, a_1\} $ 3. $ 0 \le y_j \le k_2 $ for all $ j \in \{1, \dots, a_2\} $ **Objective** Determine: - Minimum number of players sent off: $$ \min \left( \sum_{i=1}^{a_1} \mathbf{1}_{\{x_i \ge k_1\}} + \sum_{j=1}^{a_2} \mathbf{1}_{\{y_j \ge k_2\}} \right) $$ - Maximum number of players sent off: $$ \max \left( \sum_{i=1}^{a_1} \mathbf{1}_{\{x_i \ge k_1\}} + \sum_{j=1}^{a_2} \mathbf{1}_{\{y_j \ge k_2\}} \right) $$