CF1878E Iva & Pav

Iva and Pav are a famous Serbian competitive programming couple. In Serbia, they call Pav "papuca" and that's why he will make all of Iva's wishes come true. Iva gave Pav an array $ a $ of $ n $ elements. Let's define $ f(l, r) = a_l \ \& \ a_{l+1} \ \& \dots \& \ a_r $ (here $ \& $ denotes the [bitwise AND operation](http://tiny.cc/bitwise_and)). Note that $ f(l, r) $ is not defined when $ l>r $ . Iva also gave Pav $ q $ queries. Each query consists of 2 numbers, $ k $ and $ l $ , and she wants Pav to find the largest index $ r $ ( $ l \le r \le n $ ), such that $ f(l, r) \ge k $ . Pav wants to solve this problem fast because he doesn't want to upset Iva. He needs your help.

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. The first line of each test case contains a single integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ) — the length of array $ a $ . The second line of each test case contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le 10^9 $ ) — the elements of array $ a $ . The third line of each test case contains a single integer $ q $ ( $ 1 \le q \le 10^5 $ ) — the number of queries Iva gave Pav. The next $ q $ lines of each test case contains two numbers, $ l $ and $ k $ ( $ 1 \le l \le n $ , $ 1 \le k \le 10^9 $ ) — the left bound for the subsegment, and the integer $ k $ described in statement. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ . Also, it is guaranteed that the sum of $ q $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each query output maximal index $ r $ ( $ l \le r \le n $ ) such that $ a_l \ \& \ a_{l+1} \ \& \dots \& \ a_r \ \ge \ k $ . If such $ r $ doesn't exist, output $ -1 $ .

In the first test case $ n=5 $ , and the array $ a = [15, 14, 17, 42, 34] $ The first query asks for the biggest index $ r $ such that the $ f(1, r) \ge 7 $ . $ f(1,1) = 15, \ f(1, 2) = 14, \ f(1,3)=0 \ f(1, 4)=0 \ f(1, 5)=0 $ , so $ r=2 $ is the answer. The second query asks for $ f(2, r) \ge 15 $ . Since such $ r $ doesn't exist, the answer is $ -1 $ . The third query asks for $ f(4, r) \ge 5 $ . $ f(4, 4) = 42, \ f(4, 5) = 34 $ , so $ r=5 $ is the answer. In the second test case $ n=5 $ , and the array $ a= [7, 5, 3, 1, 7] $ . For the first query, $ f(1, r) \ge 7 $ . $ f(1, 1)=7, \ f(1, 2)=5, \ f(1, 3) = 1, \ f(1,4) = 1, \ f(1, 5)=1 $ , so the answer to this query is $ 1 $ . For the second query, $ f(5, r) \ge 7 $ . $ f(5, 5) = 7 $ , so the answer is $ 5 $ . For the third query, $ f(2, r) \ge 3 $ . $ f(2, 2) = 5, \ f(2, 3) = 1, \ f(2, 4) = 1, \ f(2, 5) = 1 $ , so the answer is $ 2 $ .