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 java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.List;

import java.awt.*;

public class Main {

	static long sx = 0, sy = 0, mod = (long) (1e9 + 7);
	static int[][] dirs = { { 0, 1 }, { 1, 0 }, { 0, -1 }, { -1, 0 } };
	// static ArrayList<Integer>[] a;
	static ArrayList<Integer>[] g;
	static ArrayList<Integer>[] ra;
	// static int[] dp;
	static long[] fa;
	static int[] farr;
	public static PrintWriter out = new PrintWriter(System.out);
	static ArrayList<pair> pa = new ArrayList<>();
	static StringBuilder sb = new StringBuilder();
	static boolean cycle = false;
	static long m = 998244353;
	static long[] no, col;
	static String s;
	// static long k = 0, n = 0, ans = 0;
	static long cnt;
	// static long[] dp;
	// static long[] p;
	// static long[] ans;
	// static Double[][] a = new Double[2][2];
	static Double[] x;
	static Double[] y;
	static long[] d;
	static int[][] par;
	static long[] v;
	static HashMap<Integer, Integer> map;
	// static ArrayList<Integer> p;
	static int time = 0;
	static int[] id;
	static HashMap<String, Long> hm;
	static int[] ans;
	static boolean[] b;

	public static void main(String[] args) throws IOException {

		Scanner scn = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		// Reader scn = new Reader();

		int to = scn.nextInt();

		z: while (to-- != 0) {

			int n = scn.nextInt(), m = scn.nextInt();

			String s = scn.next();
			int cnt = 0;

			a = new int[n + 1];

			for (int i = 1; i <= n; i++) {

				if (s.charAt(i - 1) == '-')
					cnt--;
				else
					cnt++;

				a[i] = cnt;

			}
			preprocess(n + 1);

			StringBuilder sb = new StringBuilder();

			while (m-- != 0) {

				int l = scn.nextInt(), r = scn.nextInt();

				int val = 0;

				if (l == 1 && r == n)
					sb.append(1);

				else if (r == n) {
					int lmin = querymin(0, l - 1), lmax = querymax(0, l - 1);

					sb.append(lmax - lmin + 1);
				}

				else {
					val = a[r] - a[l - 1];

					int lmin = querymin(0, l - 1), lmax = querymax(0, l - 1);

					int rmin = querymin(r + 1, n) + (-1) * val, rmax = querymax(r + 1, n) + (-1) * val;

					int[][] mat = { { lmin, lmax }, { rmin, rmax } };

					mat = merge(mat);

					int ans = 0;

					for (int[] p : mat)
						ans += p[1] - p[0] + 1;

					sb.append(ans);
				}

				sb.append("\n");

			}

			System.out.println(sb);

		}

	}

	public static int[][] merge(int[][] a) {

		Arrays.sort(a, new comp());

		Stack<int[]> s = new Stack<>();

		for (int i = 0; i < a.length; i++) {

			if (s.size() == 0)
				s.push(a[i]);

			else {

				if (a[i][0] > s.peek()[1])
					s.push(a[i]);

				else {
					s.peek()[1] = Math.max(s.peek()[1], a[i][1]);
				}
			}
		}

		int[][] ans = new int[s.size()][2];

		for (int i = ans.length - 1; i >= 0; i--) {
			ans[i] = s.pop();
		}

		return ans;
	}

	public static class comp implements Comparator<int[]> {

		@Override

		public int compare(int[] a, int[] b) {

			return a[0] - b[0];
		}
	}

	static int[][] min;
	static int[][] max;
	static int[] a;
	static int[] log;

	public static void preprocess(int n) {

		log = new int[n + 1];
		log[1] = 0;

		for (int i = 2; i < log.length; i++)
			log[i] = log[i / 2] + 1;

		min = new int[n][log[n] + 3];
		max = new int[n][log[n] + 3];
		for (int j = 0; (1 << j) <= a.length; j++)
			for (int i = 0; i + (1 << j) - 1 < a.length; i++) {

				if (j == 0) {
					min[i][j] = a[i];
					max[i][j] = a[i];
				}

				else {

					min[i][j] = Math.min(min[i][j - 1], min[i + (1 << (j - 1))][j - 1]);
					max[i][j] = Math.max(max[i][j - 1], max[i + (1 << (j - 1))][j - 1]);
				}
			}
	}

	public static int querymin(int l, int r) {

		int len = log[r - l + 1];

		return Math.min(min[l][len], min[r - (1 << len) + 1][len]);
	}

	public static int querymax(int l, int r) {

		int len = log[r - l + 1];

		return Math.max(max[l][len], max[r - (1 << len) + 1][len]);
	}
	// _________________________TEMPLATE_____________________________________________________________

	public static long lcm(long x, long y) {

		return (x * y) / gcd(x, y);
	}

	private static long gcd(long x, long y) {
		if (x == 0)
			return y;

		return gcd(y % x, x);
	}
	//
	// static class comp implements Comparator<Integer> {
	//
	// @Override
	// public int compare(Integer p1, Integer p2) {
	//
	// if (!hm1.contains(p1))
	// return -1;
	// else if (!hm1.contains(p2))
	// return 1;
	// else
	// return 0;
	//
	// }
	// }
	//
	// }
	//
	// public static long pow(long a, long b) {
	//
	// if (b < 0)
	// return 0;
	//
	// if (b == 0 || b == 1)
	// return (long) Math.pow(a, b);
	//
	// if (b % 2 == 0) {
	//
	// long ret = pow(a, b / 2);
	// ret = (ret % mod * ret % mod) % mod;
	// return ret;
	// }
	//
	// else {
	// return ((pow(a, b - 1) % mod) * a % mod) % mod;
	// }
	// }

	private static class pair implements Comparable<pair> {

		int i, a, b;

		pair(int c, int d, int e) {

			i = c;
			a = d;
			b = e;
		}

		@Override
		public int compareTo(pair o) {

			return this.b - o.b;
		}

		@Override

		public String toString() {

			return i + " " + a + " " + b;
		}

		// @Override
		//
		// public int hashCode() {
		// return (int) (a * 17+);
		// }
		//
		// @Override
		//
		// public boolean equals(Object o) {
		//
		// pair p = (pair) o;
		// return this.a == p.a;
		// }
		//
		// @Override
		//
		// public String toString() {
		// return this.a + " ";
		// }

	}

	private static String reverse(String s) {

		return new StringBuilder(s).reverse().toString();
	}

	public static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException {
			byte[] buf = new byte[1000000 + 1]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}

		public int[] nextIntArray(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		public int[][] nextInt2DArray(int m, int n) throws IOException {
			int[][] arr = new int[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}

		public long[][] nextInt2DArrayL(int m, int n) throws IOException {
			long[][] arr = new long[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}
		// kickstart - Solution
		// atcoder - Main
	}

}