CF1737G Ela Takes Dancing Class

DTL engineers love partying in the weekend. Ela does, too! Unfortunately, she didn't know how to dance yet. Therefore, she decided to take a dancing class.There are $ n $ students in the dancing class, including Ela. In the final project, $ n $ students will participate in a choreography described below. $ n $ students are positioned on the positive side of the $ Ox $ -axis. The $ i $ -th dancer is located at $ a_i > 0 $ . Some dancers will change positions during the dance (we'll call them movable dancers), and others will stay in the same place during a choreography (we'll call them immovable dancers). We distinguish the dancers using a binary string $ s $ of length $ n $ : if $ s_i $ equals '1', then the $ i $ -th dancer is movable, otherwise the $ i $ -th dancer is immovable. Let's call the "positive energy value" of the choreography $ d > 0 $ . The dancers will perform "movements" based on this value. Each minute after the dance begins, the movable dancer with the smallest $ x $ -coordinate will start moving to the right and initiate a "movement". At the beginning of the movement, the dancer's energy level will be initiated equally to the positive energy value of the choreography, which is $ d $ . Each time they move from some $ y $ to $ y+1 $ , the energy level will be decreased by $ 1 $ . At some point, the dancer might meet other fellow dancers in the same coordinates. If it happens, then the energy level of the dancer will be increased by $ 1 $ . A dancer will stop moving to the right when his energy level reaches $ 0 $ , and he doesn't share a position with another dancer. The dancers are very well-trained, and each "movement" will end before the next minute begins. To show her understanding of this choreography, Ela has to answer $ q $ queries, each consisting of two integers $ k $ and $ m $ . The answer to this query is the coordinate of the $ m $ -th dancer of both types from the left at $ k $ -th minute after the choreography begins. In other words, denote $ x_{k, 1}, x_{k, 2}, \dots, x_{k, n} $ as the sorted coordinates of the dancers at $ k $ -th minute from the beginning, you need to print $ x_{k, m} $ .

The first line contains three integers $ n $ , $ d $ and $ q $ ( $ 1 \le n \le 10^5 $ ; $ 1 \le d \le 10^9 $ ; $ 1 \le q \le 10^5 $ ) — the number of dancers, the positive energy value of the choreography, and the number of queries. The second line contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_1 < a_2 < \dots < a_n \le 10^9 $ ) — the coordinates of each dancer. The third line contains a binary string $ s $ of length $ n $ — the movability of each dancer. Each character is either '0' or '1'. It is guaranteed that $ s $ contains at least one character '1'. Then $ q $ lines follow, the $ i $ -th of them contains two integers $ k_i $ and $ m_i $ ( $ 1 \le k_i \le 10^9 $ , $ 1 \le m_i \le n $ ) — the content of each query.

Output $ q $ lines, each contains a single integer — the answer for the corresponding query.

Let's consider the first example test case. In the first minute, $ 1 $ is the lowest coordinate between movable dancers. The energy level is initiated with $ 3 $ . Then the following happens: - The dancer moves from $ 1 $ to $ 2 $ . The energy level decreased to $ 2 $ . - The dancer moves from $ 2 $ to $ 3 $ . The energy level decreased to $ 1 $ , then increased to $ 2 $ when she met another dancer at $ 3 $ . - The dancer moves from $ 3 $ to $ 4 $ . The energy level decreased to $ 1 $ . - The dancer moves from $ 4 $ to $ 5 $ . The energy level decreased to $ 0 $ . At the end of the first minute, the sorted coordinates of the dancers become $ [3, 5, 6, 7] $ , and their respective movability is '0111'. In the second minute, $ 5 $ is the lowest coordinate between movable dancers. The energy level is initiated with $ 3 $ . Then the following happens: - The dancer moves from $ 5 $ to $ 6 $ . The energy level decreased to $ 2 $ , then increased to $ 3 $ when she met another dancer at $ 6 $ . - The dancer moves from $ 6 $ to $ 7 $ . The energy level decreased to $ 2 $ , then increased to $ 3 $ when she met another dancer at $ 7 $ . - The dancer moves from $ 7 $ to $ 8 $ . The energy level decreased to $ 2 $ . - The dancer moves from $ 8 $ to $ 9 $ . The energy level decreased to $ 1 $ . - The dancer moves from $ 9 $ to $ 10 $ . The energy level decreased to $ 0 $ . At the end of the second minute, the sorted coordinates of the dancers become $ [3, 6, 7, 10] $ , and their respective movability is '0111'.