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.awt.*;
import java.io.*;
import java.io.IOException;
import java.util.*;
import java.text.DecimalFormat;
 
public class Exam {
	
	public static long mod = (long)Math.pow(10, 9)+7 ;
	public static double epsilon=0.00000000008854;//value of epsilon
	public static InputReader sc = new InputReader(System.in);
	public static PrintWriter pw = new PrintWriter(System.out);
	public static long gcd(long a,long b){
		while(b>0){
			long t=b;
			b=a%b;
			a=t;
		}
		return a;
    }
	
	static void dfs(Point p[],int v,boolean vis[]){
        if (vis[v])return;
        vis[v]=true;
        for (int i=0;i<p.length;i++){
            if (p[i].x==p[v].x || p[i].y==p[v].y){
                dfs(p,i,vis);
            }
        }
	}
	public static long bSearch(Pair[]d, int l, int r, int a) {
		if(d[l].d > a)
			return 0;
		if(l == r)
			return d[l].g;
		int m = (l + r + 1) / 2;
		if(d[m].d > a)
			return bSearch(d, l, m - 1, a);
		return bSearch(d, m, r, a);
	}
	static class Pair implements Comparable<Pair> {
		int d, i;
		long g;
		public Pair(int D, long G, int I) {
			d = D;
			g = G;
			i = I;
		}
		public int compareTo(Pair p) {
			if(d == p.d)
				return i - p.i;
			return d - p.d;
		}
	 }
	 
	 static void dfs(int src, ArrayList<ArrayList<Integer>> list, int vis[],int c[])
    {
        //Here 0-white,1-gray & 2-black;
       // Time complexity O(n+m)
       //System.out.print(src+" ");
	   vis[src]=1;
       for(int i=0;i<list.get(src).size();i++){
           if(vis[list.get(src).get(i)]==0){
               dfs(list.get(src).get(i),list, vis,c);
           }
	   }
	   c[0]++;
       vis[src]=2;
    }
	public static long pow(long x,long y,long mod){
		long ans=1;
		while(y>0){
			if((y&1)==1){
				ans=(ans*x)%mod;
			}
			y=y>>1;
			x=(x*x)%mod;
		}
		return ans;
    } 
	 
	public static void main(String[] args) {
		// code starts..
			int q=sc.nextInt();
			while(q-->0){
				int n=sc.nextInt();
				int m=sc.nextInt();
				int z=n-m;
				if(m==0)
				{
					pw.println(0);
					continue;
				}
			
				long t=((long)n*(n+1))/2;

				if(z<=m+1){
					t-=z;
				}
				else{
					int f=z/(m+1);
					long m1=m+1-z%(m+1);
					long m2=z%(m+1);


					long f1=(m1)*((long)f*(f+1))/2;
					f++;
					f1+=m2*((long)f*(f+1))/2;
					t-=f1;
					
				}
				pw.println(t);
			}

		// Code ends...
		pw.flush();
		pw.close();
	}
	static class tripletL implements Comparable<tripletL> {
		Long x, y, z;
 
		tripletL(long x, long y, long z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}
 
		public int compareTo(tripletL o) {
			int result = x.compareTo(o.x);
			if (result == 0)
				result = y.compareTo(o.y);
			if (result == 0)
				result = z.compareTo(o.z);
 
			return result;
		}
 
		public boolean equlas(Object o) {
			if (o instanceof tripletL) {
				tripletL p = (tripletL) o;
				return (x - p.x == 0) && (y - p.y ==0 ) && (z - p.z == 0);
			}
			return false;
		}
 
		public String toString() {
			return x + " " + y + " " + z;
		}
 
		public int hashCode() {
			return new Long(x).hashCode() * 31 + new Long(y).hashCode() + new Long(z).hashCode();
		}
	}
	public static String Doubleformate(double a,int n){
		String s="";
		while(n-->0){
			s+='0';
		}
		DecimalFormat f =new DecimalFormat("#0."+s);
		return f.format(a);
	}
 
	public static Comparator<Integer[]> column(int i){
		return 
		new Comparator<Integer[]>() {
			@Override
			public int compare(Integer[] o1, Integer[] o2) {
				return o1[i].compareTo(o2[i]);//for ascending
				//return o2[i].compareTo(o1[i]);//for descending
			}
		};
	}
	public static Comparator<Integer[]> pair(){
		return 
		new Comparator<Integer[]>() {
			@Override
			public int compare(Integer[] o1, Integer[] o2) {
				int result=o1[0].compareTo(o2[0]);
				if(result==0)
				result=o1[1].compareTo(o2[1]);
				return result;
			}
		};
	}
	public static Comparator<Integer[]> Triplet(){
		return 
		new Comparator<Integer[]>() {
			@Override
			public int compare(Integer[] o1, Integer[] o2) {
			
					for(int i=0;i<3;i++){
						for(int j=i+1;j<3;j++){
							for(int k=0;k<3;k++){
								for(int p=k+1;p<3;p++){
									if((o1[i]==o2[k]&&o1[j]==o2[p])||(o1[j]==o2[k]&&o1[i]==o2[p])){
 
									}
								}
							}
						}
					}
					int result=o1[0].compareTo(o2[0]);
					if(result==0)
					result=o1[1].compareTo(o2[1]);
					if(result==0)
					result=o1[2].compareTo(o2[2]);
					return result;
			}
		};
	}
	
	
	public static String reverseString(String s){
		StringBuilder input1 = new StringBuilder(); 
        input1.append(s);  
		input1 = input1.reverse();
		return input1.toString();
	}
	public static int[] scanArray(int n){
		int a[]=new int [n];
		for(int i=0;i<n;i++)
		a[i]=sc.nextInt();
 
		return a;
	}
	public static long[] scanLongArray(int n){
		long a[]=new long [n];
		for(int i=0;i<n;i++)
		a[i]=sc.nextLong();
 
		return a;
	}
	public static String [] scanStrings(int n){
		String a[]=new String [n];
		for(int i=0;i<n;i++)
		a[i]=sc.nextLine();
 
		return a;
	}
	static class InputReader {
 
		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;
 
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
 
		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
 
		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}
 
		public String readString() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}
 
		public String nextLine() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isEndOfLine(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;
		}
 
		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
 
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
 
}
class p{
	int a,b,c;
}
class SegmentTree{
	int s[],n, t;
	SegmentTree(int a[]){
		n=a.length;
		int l=(int)Math.ceil(Math.log(n)/Math.log(2));
		if(l%2==0)
		t=1;
		else
		t=0;
		l=2*(int)Math.pow(2,l)-1;
		s=new int[l];
		createSegmentTreeUtil(a, 0, 0, n-1,t);
	}
	
	int createSegmentTreeUtil(int a[],int root,int l,int r,int c){
		if(l==r)
		s[root]=a[l];
		else
		s[root]= Compare(createSegmentTreeUtil(a, 2*root+1, l, (l+r)/2,c^1), createSegmentTreeUtil(a,2*root+2, (l+r)/2+1,r,c^1),c);
		return s[root];
	}
	int getValue(){
		return s[0];
	}
	
	int update(int p,int k){
		return updateUtil(p, k,0,0,n-1,t);
	}
	int updateUtil(int p,int k,int root,int l,int r,int c){
		if(l==r&&l==k){
			s[root]=p;
			return s[root];
		}
		else if(l>k||r<k)
		return s[root];
		else{
			s[root]=Compare(updateUtil(p, k, 2*root+1, l, (l+r)/2,c^1), updateUtil(p, k, 2*root+2,(l+r)/2+1,r,c^1),c);
			return s[root];
		}
	}


	int Compare(int a,int b,int c){
		if(c==0)
		return a|b;
		else
		return a^b;
	}
}

class spair{
	String s1;
	String s2;
	spair(String r1,String r2){
		s1=r1;
		s2=r2;
	}
}

