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. 
import sys
for tc in range(int(input())):
    n, m = map(int, input().split())
    p = input()
    pp = p[::-1]
    a = [[0, 0, 0] for i in range(n+1)]
    ap = [[0, 0, 0] for i in range(n+1)]
    x = 0
    mxx = 0
    mnx = 0
    for i in range(n):
        if p[i] == "+":
            x += 1
            mxx = max(mxx, x)
        else:
            x -= 1
            mnx = min(mnx, x)
        a[i+1][0] = x
        a[i+1][1] = mxx
        a[i+1][2] = mnx
    
    xp = 0
    mnxp = 0
    mxxp = 0
    for i in range(n):
        if pp[i] == "+":
            xp -= 1
            mnxp = min(mnxp, xp)
        else:
            xp += 1
            mxxp = max(mxxp, xp)
        ap[i+1][0] = xp
        ap[i+1][1] = mxxp
        ap[i+1][2] = mnxp
    
    for i in range(m):
        l, r = map(int, sys.stdin.readline().strip().split())
        xs = a[l-1][0]
        mxs = a[l-1][1]
        mns = a[l-1][2]
        r = n - r
        xr = ap[r][0]
        mxr = ap[r][1]
        mnr = ap[r][2]
        d = xs - xr
        mxr += d
        mnr += d
        mx = max(mxs, mxr)
        mn = min(mns, mnr)
        print(mx-mn+1)