链接：https://codeforces.ml/contest/1301/problem/C

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

More formally, f(s)f(s) is equal to the number of pairs of integers (l,r)(l,r), such that 1≤l≤r≤|s|1≤l≤r≤|s| (where |s||s| is equal to the length of string ss), such that at least one of the symbols sl,sl+1,…,srsl,sl+1,…,sr is equal to "1".

For example, if s=s="01010" then f(s)=12f(s)=12, because there are 1212 such pairs (l,r)(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)(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 nn and mm and asked him this problem. For all binary strings ss of length nn which contains exactly mm symbols equal to "1", find the maximum value of f(s)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 tt (1≤t≤1051≤t≤105)  — the number of test cases. The description of the test cases follows.

The only line for each test case contains two integers nn, mm (1≤n≤1091≤n≤109, 0≤m≤n0≤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)f(s) over all strings ss of length nn, which has exactly mm symbols, equal to "1".

Example


input

Copy

5
3 1
3 2
3 3
4 0
5 2

output

Copy

4
5
6
0
12

Note

In the first test case, there exists only 33 strings of length 33, which has exactly 11 symbol, equal to "1". These strings are: s1=s1="100", s2=s2="010", s3=s3="001". The values of ff for them are: f(s1)=3,f(s2)=4,f(s3)=3f(s1)=3,f(s2)=4,f(s3)=3, so the maximum value is 44 and the answer is 44.

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

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

In the fourth test case, the only string ss of length 44, which has exactly 00 symbols, equal to "1" is "0000" and the value of ff for that string is 00, so the answer is 00.

In the fifth test case, the string ss with the maximum value is "01010" and it is described as an example in the problem statement.

题解：又一次体会到了打完比赛知道怎么写的悲惨遭遇QAQ，简单来说就是划分0，1将0等分成k个区间，然后要用到容斥的思想我们先求出最大可能值，只需要减去不可能的情况就可

#include<bits/stdc++.h>
using namespace std;
long long t,n,m,l,r,x,s,k;
int main()
{
	cin>>t;
	while(t--)
	{
		cin>>n>>m;
		k=(n-m)/(m+1);
		l=(n-m)%(m+1);
		s=n*(n+1)/2;
		s-=(k*(k+1)/2)*(m+1); 
		s-=(k+1)*l;
		cout<<s<<endl;
	}
}