You 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? 

Input

The first line contains a single integer t (1 ≤ t ≤ 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 ≤ n, m ≤ 2 ⋅ 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 ≤ l ≤ r ≤ n) — the description of the query.

The sum of n over all testcases doesn't exceed 2 ⋅ 10^5. The sum of m over all testcases doesn't exceed 2 ⋅ 10^5. 

Output

For 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.

Example

Input


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

Note

The instructions that remain for each query of the first testcase are: 

  1. empty program — x was only equal to 0; 
  2. "-" — x had values 0 and -1; 
  3. "---+" — x had values 0, -1, -2, -3, -2 — there are 4 distinct values among them; 
  4. "+--+--+" — the distinct values are 1, 0, -1, -2. 
'''
#python-io
'''

import sys

# need this
input = sys.stdin.readline 

MAXN = 2 * 100_000 + 5
cnt, top, bot = [0]*MAXN, [[0]*MAXN for i in range(2)], [[0]*MAXN for i in range(2)]

def program(n, m, s):
	for i in range(n):
		if s[i] == '+': cnt[i+1] = cnt[i] + 1
		else: cnt[i+1] = cnt[i] - 1
	for i in range(1, n+1):
		top[0][i] = bot[0][i] = top[1][i] = bot[1][i] = cnt[i]	
	for i in range(1, n+1):
		top[0][i] = max(top[0][i], top[0][i-1])
		bot[0][i] = min(bot[0][i], bot[0][i-1])	
	for i in range(n-1, -1, -1):
		top[1][i] = max(top[1][i], top[1][i+1])
		bot[1][i] = min(bot[1][i], bot[1][i+1])

	for _ in range(m):
		# strip() removes any whitespace (???)
		l, r = map(int, input().strip().split())
		diff = cnt[l-1] - cnt[r]
		if r < n:
			t = max(top[0][l-1], top[1][r+1] + diff)
			b = min(bot[0][l-1], bot[1][r+1] + diff)
		else:
			t, b = top[0][l-1], bot[0][l-1]
		print(str(t-b+1) + '\n')
		

def main():
	for t in range(int(input().strip())):
		n, m = map(int, input().strip().split())
		s = input().strip()
		program(n, m, s)

if __name__ == "__main__":
    main()