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 os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
 
 
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
 
 
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")

import typing

def _ceil_pow2(n: int) -> int:
    x = 0
    while (1 << x) < n:
        x += 1

    return x


def _bsf(n: int) -> int:
    x = 0
    while n % 2 == 0:
        x += 1
        n //= 2

    return x

class SegTree:
    def __init__(self,
                 op: typing.Callable[[typing.Any, typing.Any], typing.Any],
                 e: typing.Any,
                 v: typing.Union[int, typing.List[typing.Any]]) -> None:
        self._op = op
        self._e = e

        if isinstance(v, int):
            v = [e] * v

        self._n = len(v)
        self._log = _ceil_pow2(self._n)
        self._size = 1 << self._log
        self._d = [e] * (2 * self._size)

        for i in range(self._n):
            self._d[self._size + i] = v[i]
        for i in range(self._size - 1, 0, -1):
            self._update(i)

    def set(self, p: int, x: typing.Any) -> None:
        assert 0 <= p < self._n

        p += self._size
        self._d[p] = x
        for i in range(1, self._log + 1):
            self._update(p >> i)

    def get(self, p: int) -> typing.Any:
        assert 0 <= p < self._n

        return self._d[p + self._size]

    def prod(self, left: int, right: int) -> typing.Any:
        assert 0 <= left <= right <= self._n
        sml = self._e
        smr = self._e
        left += self._size
        right += self._size

        while left < right:
            if left & 1:
                sml = self._op(sml, self._d[left])
                left += 1
            if right & 1:
                right -= 1
                smr = self._op(self._d[right], smr)
            left >>= 1
            right >>= 1

        return self._op(sml, smr)

    def all_prod(self) -> typing.Any:
        return self._d[1]

    def max_right(self, left: int,
                  f: typing.Callable[[typing.Any], bool]) -> int:
        assert 0 <= left <= self._n
        assert f(self._e)

        if left == self._n:
            return self._n

        left += self._size
        sm = self._e

        first = True
        while first or (left & -left) != left:
            first = False
            while left % 2 == 0:
                left >>= 1
            if not f(self._op(sm, self._d[left])):
                while left < self._size:
                    left *= 2
                    if f(self._op(sm, self._d[left])):
                        sm = self._op(sm, self._d[left])
                        left += 1
                return left - self._size
            sm = self._op(sm, self._d[left])
            left += 1

        return self._n

    def min_left(self, right: int,
                 f: typing.Callable[[typing.Any], bool]) -> int:
        assert 0 <= right <= self._n
        assert f(self._e)

        if right == 0:
            return 0

        right += self._size
        sm = self._e

        first = True
        while first or (right & -right) != right:
            first = False
            right -= 1
            while right > 1 and right % 2:
                right >>= 1
            if not f(self._op(self._d[right], sm)):
                while right < self._size:
                    right = 2 * right + 1
                    if f(self._op(self._d[right], sm)):
                        sm = self._op(self._d[right], sm)
                        right -= 1
                return right + 1 - self._size
            sm = self._op(self._d[right], sm)

        return 0

    def _update(self, k: int) -> None:
        self._d[k] = self._op(self._d[2 * k], self._d[2 * k + 1])
 
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

t=int(input())
for _ in range(t):
  n,m=map(int,input().split())
  s=input()
  a=[0]
  curr=0
  for i in range(n):
    if s[i]=='+':
      curr+=1
    else:
      curr-=1
    a.append(curr)
  segtreemax=SegTree(max,-10**9,a)
  segtreemin=SegTree(min,10**9,a)
  for i in range(m):
    l,r=map(int,input().split())
    max1=segtreemax.prod(0,l)
    min1=segtreemin.prod(0,l)
    if r<n:
      max1=max(max1,a[l-1]+segtreemax.prod(r+1,n+1)-a[r])
      min1=min(min1,a[l-1]+segtreemin.prod(r+1,n+1)-a[r])
    print(max1-min1+1)