CF2184G Nastiness of Segments

Andrey remembered that he has $ n $ blocks numbered from $ 1 $ to $ n $ . On the block with number $ i $ , there is initially an integer $ a_i $ written. He arranged them in a row in increasing order of their numbers: first is the block with number $ 1 $ , then the block with number $ 2 $ , and so on, with the block with number $ n $ at the end. For a certain segment of consecutive blocks $ [l, r] $ ( $ 1 \le l \le r \le n $ ), we call an integer $ d\ (0 \le d \le r-l) $ nasty if $ \min(a_l, a_{l+1}, \ldots, a_{l+d}) = d $ . Andrey is very curious, so he wants to perform $ q $ operations of one of two types: 1. Change the number $ a_i $ written on the $ i $ -th block to $ x $ . 2. Determine the nastiness of the segment $ [l,\ r]\ (1 \le l \le r \le n) $ . The nastiness of the segment refers to the number of nasty numbers $ d\ (0 \le d \le r-l) $ for the given segment. Andrey couldn't figure out how to process these queries quickly, so he turned to you for help. Help him perform the actions described above!

The first line contains an integer $ t $ $ (1 \le t \le 10^4) $ — the number of test cases. The first line of each test case contains two integers $ n $ and $ q $ $ (1 \le n, q \le 2 \cdot 10^5) $ — the number of blocks and the number of operations, respectively. The next line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ $ (1 \le a_i \le 2 \cdot 10^5) $ — the initial numbers written on the blocks. The following $ q $ lines describe the operations to be performed. Each line starts with an integer $ idx $ $ (1 \le idx \le 2) $ — the type of operation. If $ idx = 1 $ , then two integers $ i $ $ (1 \le i \le n) $ and $ x $ $ (1 \le x \le 2 \cdot 10^5) $ follow — the description of the first type of operation. If $ idx = 2 $ , then two integers $ l $ and $ r $ $ (1 \le l \le r \le n) $ follow — the description of the second type of operation. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ , and the sum of $ q $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, for each operation of the second type, print an integer representing the nastiness of the segment.