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. 
from sys import stdin, stdout

INF = float('inf')

tc = input()
inp = stdin.readlines()
out = []

ptr = 0
while ptr < len(inp):
    n, m = map(int, inp[ptr].strip().split()); ptr += 1

    ops = inp[ptr].strip(); ptr += 1

    # [min, max, val]
    pre = [[INF, -INF, 0] for i in xrange(n + 1)]

    # [min, max]
    suf = [[INF, -INF] for i in xrange(n + 1)]

    # fill pre
    for i in xrange(1, n + 1):
        c = 44 - ord(ops[i - 1])
        
        pre[i][2] = pre[i - 1][2] + c
        pre[i][1] = max(pre[i][2], pre[i - 1][1])
        pre[i][0] = min(pre[i][2], pre[i - 1][0])

    # fill suf
    
    # running variables
    sufmn, sufmx = 0, 0
    
    for i in xrange(n - 1, -1, -1):
        c = 44 - ord(ops[i])

        mn, mx = min(c, sufmn + c), max(c, sufmx + c)
        suf[i] = [mn, mx]

        # update running variables
        sufmn, sufmx = mn, mx

    for i in xrange(m):
        l, r = map(int, inp[ptr].strip().split()); ptr += 1

        X = pre[l - 1][2]

        # edge case
        sufmn = suf[r][0]
        if (sufmn == INF): sufmn = 0

        sufmx = suf[r][1]
        if (sufmx == -INF): sufmx = 0

        # range of values
        lo = min(pre[l - 1][0], X + sufmn, X + sufmx)
        hi = max(pre[l - 1][1], X + sufmn, X + sufmx)

        ans = (hi - lo + 1) + (1 - int(lo <= 0 and hi >= 0))
        out.append(str(ans))

stdout.write('\n'.join(out))
        

	     			 	 	 	 					   		  	 	