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>
 
using namespace std; 
const int inf=0x3f3f3f3f;
typedef long long ll; 
const int N=2e5+7;
const ll mod=998244353;
  
char s[N];

int sum[N],maxn2[N],minn2[N],maxn1[N],minn1[N];

int main()
{   
    int t;
    scanf("%d",&t);
    while(t--){
        int n,k,z;
        scanf("%d%d%s",&n,&k,s);
        for (int i = 1; i <= n; ++i)
        {
            if(s[i-1]=='+')sum[i]=sum[i-1]+1;
            else sum[i]=sum[i-1]-1;

            maxn1[i]=max(maxn1[i-1],sum[i]);
            minn1[i]=min(minn1[i-1],sum[i]);
        }
        maxn2[n]=minn2[n]=sum[n];
        for(int i=n-1;i>=0;i--){
            maxn2[i]=max(maxn2[i+1],sum[i]);
            minn2[i]=min(minn2[i+1],sum[i]);
        }
        while(k--){
            int l,r;
            scanf("%d%d",&l,&r);
            int maxn=maxn1[l-1],minn=minn1[l-1];
            if(maxn1[r]<=maxn1[n]){
                maxn=max(maxn,maxn2[r]-(sum[r]-sum[l-1]));
            }
            if(minn1[r]>=minn1[n]){
                minn=min(minn,minn2[r]-(sum[r]-sum[l-1]));
            } 
            cout<<maxn-minn+1<<endl;
        }
    }
    return 0;
}