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. 
#include<bits/stdc++.h>
#define ll long long 
#define ull unsigned long long int
int lfmx[200005];
int lfmi[200005];
int rfmx[200005];
int rfmi[200005];

int su[200005];
int pre[200005];
using namespace std;
void fun()
{
	int n,m;
	cin>>n>>m;
	string s;
	cin>>s;
		
	lfmx[0]=0;
	lfmi[0]=0;
	pre[0]=0;
	for (int i=0;i<n;i++)
	{
		if (s[i]=='-')
		{
			pre[i+1]=pre[i]-1;
		
		}
		else
		{
			pre[i+1]=pre[i]+1;
		}
		lfmx[i+1]=max(lfmx[i],pre[i+1]);
		lfmi[i+1]=min(lfmi[i],pre[i+1]);
	}
	
	rfmx[n+1]=0;
	rfmi[n+1]=0;
	su[n+1]=0;
	for (int i=n;i>0;i--)
	{
		int d = s[i-1] == '+' ? 1 : -1;
		rfmx[i]=max(rfmx[i+1]+d,0);
		rfmi[i]=min(rfmi[i+1]+d,0);
	}
	
	vector<int> ans;
	for (int i=0;i<m;i++)
	{
		int l,r;
		cin>> l>>r;
		
		int mini=lfmi[l-1];
		int maxi=lfmx[l-1];
		mini=min(mini,rfmi[r+1]+pre[l-1]);
		maxi=max(maxi,rfmx[r+1]+pre[l-1]);
		
		
		ans.push_back(maxi-mini+1);
	}
	for (auto i : ans)
	{
		cout<<i<<endl;
	}
}

int main()
{
	int t;
	cin>>t;
	while (t--)
	{
	 fun();
	}
 return 0;
}

