Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols "0" and "1"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to "1".

More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≤ l ≤ r ≤ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to "1". 

For example, if s = "01010" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5).

Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to "1", find the maximum value of f(s).

Mahmoud couldn't solve the problem so he asked you for help. Can you help him? 

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. The description of the test cases follows.

The only line for each test case contains two integers n, m (1 ≤ n ≤ 10^{9}, 0 ≤ m ≤ n) — the length of the string and the number of symbols equal to "1" in it.

Output

For every test case print one integer number — the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to "1".

Example

Input


5
3 1
3 2
3 3
4 0
5 2


Output


4
5
6
0
12

Note

In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to "1". These strings are: s_1 = "100", s_2 = "010", s_3 = "001". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4.

In the second test case, the string s with the maximum value is "101".

In the third test case, the string s with the maximum value is "111".

In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to "1" is "0000" and the value of f for that string is 0, so the answer is 0.

In the fifth test case, the string s with the maximum value is "01010" and it is described as an example in the problem statement.
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.*;
import java.io.*;
import java.math.*;
public class Main7
{
	static class Pair
	{ 
		int x;
		int y;
		int z;
		int p;
		public Pair(int x, int y,int z, int p) 
		{     
			this.x=x;
			this.y=y;
			this.z=z;
			this.p=p;
		}
		    
   /* @Override
            public int hashCode() 
            { 
                final int temp = 14; 
                int ans = 1; 
                ans =x*31+y*13; 
                return ans; 
            } 
      
            // Equal objects must produce the same 
            // hash code as long as they are equal 
        @Override
        public boolean equals(Object o) 
        { 
            if (this == o) { 
                return true; 
            } 
            if (o == null) { 
                return false; 
            } 
            if (this.getClass() != o.getClass()) { 
                return false; 
            } 
            Pair other = (Pair)o; 
            if (this.x != other.x || this.y!=other.y) { 
                return false; 
            } 
            return true; 
        }*/
	} 
	static class Pair1
	{
		int x;
		int y;
		long z;
		Pair1(int x, int y, long z)
		{
			this.x=x;
			this.y=y;
			this.z=z;
		}
	}
    public static long pow(long a, long b)
    {
        long result=1;
        while(b>0)
        {
            if (b % 2 != 0)
            {
                result=(result*a);
                b--;
            } 
            a=(a*a);
            b /= 2;
        }   
        return result;
    }
    public static long fact(long num)
    {
		long value=1;
		int i=0;
		for(i=2;i<num;i++)
		{
			value=((value%mod)*i%mod)%mod;
		}
		return value;
	}
	public static long gcd(long a, long b)
	{
		if (a == 0)
			return b;
		return gcd(b%a, a);
	}	
	public static long lcm(long a,long b)
	{
		return a * (b / gcd(a, b));
	}
/*   public static void dfs(int parent,boolean[] visited,int[] dp)
	{
		ArrayList<Integer> arr=new ArrayList<Integer>();
		arr=graph.get(parent);
		visited[parent]=true;
		for(int i=0;i<arr.size();i++)
		{
			int num=(int)arr.get(i);
			if(visited[num]==false)
			{
				dfs(num,visited,dp);
			}
			dp[parent]=Math.max(dp[num]+1,dp[parent]);
		}
	}
//  static int flag1=0;
	static int[] dis;*/
	static int mod=1000000007;
	static ArrayList<ArrayList<Integer>> graph;
	static ArrayList<ArrayList<Integer>> g;
/*    public static void bfs(int num,int size)
	{
		boolean[] visited=new boolean[size+1];
		Queue<Integer> q=new LinkedList<>();
		q.add(num);
		ans[num]=1;
		visited[num]=true;
		while(!q.isEmpty())
		{
			int x=q.poll();
			ArrayList<Integer> al=graph.get(x);
			for(int i=0;i<al.size();i++)
			{
				int y=al.get(i);    
				if(visited[y]==false)
				{
					q.add(y);
					ans[y]=ans[x]+1;
					visited[y]=true;
				}
			}
		}
	}
	static int[] ans;*/
	public static int[] sort(int[] a)
	{
		int n=a.length;
		ArrayList<Integer> ar=new ArrayList<>();
		for(int i=0;i<a.length;i++)
		{
			ar.add(a[i]);
		}
		Collections.sort(ar);
		for(int i=0;i<n;i++)
		{
			a[i]=ar.get(i);
		}
		return a;
	}
	static int find(int num)
	{
		if(parent[num]!=num)
		{
			parent[num]=find(parent[num]);
		}
		return parent[num];
	} 
	static void union(int x , int y ) 
	{ 
		int xroot = find(x); 
		int yroot = find(y); 
	  
		if (rank[xroot] < rank[yroot]) 
		{
			parent[xroot] = yroot; 
			size[yroot]+=size[xroot];
			size[xroot]=size[yroot];
		}
		else if (rank[yroot] < rank[xroot]) 
		{
			parent[yroot] = xroot; 
			size[xroot]+=size[yroot];
			size[yroot]=size[xroot];
		}
		else
		{ 
			parent[xroot] = yroot; 
			rank[yroot]++; 
			size[yroot]+=size[xroot];
			size[xroot]=size[yroot];
		} 
	} 
	static int[] parent;
	static int[] rank;
	static int[] size;
	static public void main(String args[])throws IOException
	{
		int tt=i();
		StringBuilder sb=new StringBuilder();
		while(tt-->0)
		{
			long n=l();
			long m=l();
			long no_of_zeroes=n-m;
			if(n%2==0)
			{
				long gaps=0;
				if(m<n/2)
				{
					gaps=m+1;
					long tmp=no_of_zeroes/gaps;
					long rem=no_of_zeroes%gaps;
					long ans=(((tmp+1)*(tmp+2))/2)*rem+((tmp*(tmp+1))/2)*(gaps-rem);
					ans=n*(n+1)/2-ans;
					sb.append(ans+"\n");
			//		pln(ans+"");
				}
				else
				{
					gaps=n/2-(m-n/2);
					if(gaps==0)
					{
						long ans=n*(n+1)/2;
						
					sb.append(ans+"\n");
				//		pln(ans+"");
					}
					else
					{
						long tmp=no_of_zeroes/gaps;
						long rem=no_of_zeroes%gaps;	
						long ans=(((tmp+1)*(tmp+2))/2)*rem+((tmp*(tmp+1))/2)*(gaps-rem);
						ans=n*(n+1)/2-ans;
						
					sb.append(ans+"\n");
					//	pln(ans+"");
					}
				}
			}
			else
			{
				long gaps=0;
				if(m<=n/2)
				{
					gaps=m+1;
					long tmp=no_of_zeroes/gaps;
					long rem=no_of_zeroes%gaps;
					long ans=(((tmp+1)*(tmp+2))/2)*rem+((tmp*(tmp+1))/2)*(gaps-rem);
					ans=n*(n+1)/2-ans;
					
					sb.append(ans+"\n");
			//		pln(ans+"");
				}
				else
				{
					gaps=n/2+1-(m-n/2);
					if(gaps==0)
					{
						long ans=(n*(n+1))/2;
						
					sb.append(ans+"\n");
					//	pln(ans+"");
					}
					else
					{
						long tmp=no_of_zeroes/gaps;
						long rem=no_of_zeroes%gaps;
						long ans=(((tmp+1)*(tmp+2))/2)*rem+((tmp*(tmp+1))/2)*(gaps-rem);
						ans=n*(n+1)/2-ans;
						
					sb.append(ans+"\n");
					}
				}
			}
		}
		System.out.print(sb.toString());
	} 
			/**/
	static InputReader in=new InputReader(System.in);
	static OutputWriter out=new OutputWriter(System.out);
	public static long l()
	{
		String s=in.String();
		return Long.parseLong(s);
	}
	public static void pln(String value)
	{
		System.out.println(value);
	}
	public static int i()
	{
		return in.Int();
	}
	public static String s()
	{
		return in.String();
	}
}
	class InputReader 
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
	 
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
	 
		public int read() {
			if (numChars== -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
	 
		public int Int() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
	 
		public String String() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}
	 
		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	 
		public String next() {
			return String();
		}
	 
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
	 
	class OutputWriter {
		private final PrintWriter writer;
	 
		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}
	 
		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}
	 
		public void print(Object...objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}
	 
		public void printLine(Object...objects) {
			print(objects);
			writer.println();
		}
	 
		public void close() {
			writer.close();
		}
	 
		public void flush() {
			writer.flush();
		}
	 
		}
	 
		class IOUtils {
	 
		public static int[] readIntArray(InputReader in, int size) {
			int[] array = new int[size];
			for (int i = 0; i < size; i++)
				array[i] = in.Int();
			return array;
		}
	 
	} 

