D. Programtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a program that consists of n instructions. Initially a single variable x is assigned to 0. Afterwards, the instructions are of two types:   increase x by 1;  decrease x by 1. You are given m queries of the following format:   query l r — how many distinct values is x assigned to if all the instructions between the l-th one and the r-th one inclusive are ignored and the rest are executed without changing the order? InputThe first line contains a single integer t (1 \le t \le 1000) — the number of testcases.Then the description of t testcases follows.The first line of each testcase contains two integers n and m (1 \le n, m \le 2 \cdot 10^5) — the number of instructions in the program and the number of queries.The second line of each testcase contains a program — a string of n characters: each character is either '+' or '-' — increment and decrement instruction, respectively.Each of the next m lines contains two integers l and r (1 \le l \le r \le n) — the description of the query.The sum of n over all testcases doesn't exceed 2 \cdot 10^5. The sum of m over all testcases doesn't exceed 2 \cdot 10^5. OutputFor each testcase print m integers — for each query l, r print the number of distinct values variable x is assigned to if all the instructions between the l-th one and the r-th one inclusive are ignored and the rest are executed without changing the order.ExampleInput
2
8 4
-+--+--+
1 8
2 8
2 5
1 1
4 10
+-++
1 1
1 2
2 2
1 3
2 3
3 3
1 4
2 4
3 4
4 4
Output
1
2
4
4
3
3
4
2
3
2
1
2
2
2
NoteThe instructions that remain for each query of the first testcase are:   empty program — x was only equal to 0;  "-" — x had values 0 and -1;  "---+" — x had values 0, -1, -2, -3, -2 — there are 4 distinct values among them;  "+--+--+" — the distinct values are 1, 0, -1, -2. 
2
8 4
-+--+--+
1 8
2 8
2 5
1 1
4 10
+-++
1 1
1 2
2 2
1 3
2 3
3 3
1 4
2 4
3 4
4 4

1 2 4 4 3 3 4 2 3 2 1 2 2 2 
['data structures', 'dp', 'implementation', 'strings', '*1700']