You are given two integers (n) and (m). For a sequence of (n) integers (A=(a_1, a_2, \ldots, a_n)), the parallel sums of (A) are the (n-m+1) integers (s_1, s_2, \ldots, s_{n-m+1}) defined by (s_i = a_i + a_{i+1} + \ldots + a_{i+m-1}) for each (i) ((1 \leq i \leq n-m+1)). You are given the values of (s_1, s_2, \ldots, s_{n-m+1}). Your task is to answer (q) queries, described as follows. In the (j)-th query, you are given two integers (l_j) and (r_j), and you are asked to find the smallest possible value of (\max(a_{l_j}, a_{l_j+1}, \ldots, a_{r_j})) among all sequences (A=(a_1, a_2, \ldots, a_n)) of (n) integers (possibly negative) such that (s_1, s_2, \ldots, s_{n-m+1}) are the parallel sums of (A). Or determine if this value can be arbitrarily small. The first line of input contains two integers (n) and (m) ((1 \leq m \leq n \leq 200\,000)). The second line contains (n-m+1) integers (s_1, s_2, \ldots, s_{n-m+1}) ((-10^9 \leq s_i \leq 10^9)). The third line contains a single integer (q) ((1 \leq q \leq 100\,000)). The (j)-th of the next (q) lines contains two integers (l_j) and (r_j) ((1 \leq l_j \leq r_j \leq n)). Output (q) lines. The (j)-th line should contain the smallest possible value of (\max(a_{l_j}, a_{l_j+1}, \ldots, a_{r_j})). If that value can be arbitrarily small, output unbounded instead. Explanation for the sample input/output #1 For the first query, take (A = (9, -4, -3, 2, 1, 2, 1, 1)). The parallel sums of (A) are ((4, -4, 2, 6, 5)) as required. Then (\max(a_3, \ldots, a_7) = \max(-3, 2, 1, 2, 1) = 2). It can be shown that (2) is the smallest possible value. For the second query, you can make the value arbitrarily small. For the third query, take (A = (4, -3, 0, 3, -4, 3, 4, 2)). Then (\max(4, -3, 0, 3, -4, 3, 4, 2) = 4), which is the smallest possible value.