There are n people participating in some contest, they start participating in x minutes intervals. That means the first participant starts at time 0, the second participant starts at time x, the third — at time 2 ⋅ x, and so on.

Duration of contest is t minutes for each participant, so the first participant finishes the contest at time t, the second — at time t + x, and so on. When a participant finishes the contest, their dissatisfaction equals to the number of participants that started the contest (or starting it now), but haven't yet finished it.

Determine the sum of dissatisfaction of all participants.

Input

The first line contains a single integer k (1 ≤ k ≤ 1000) — the number of test cases.

Each of the next k lines contains three integers n, x, t (1 ≤ n, x, t ≤ 2 ⋅ 10^9) — the number of participants, the start interval and the contest duration.

Output

Print k lines, in the i-th line print the total dissatisfaction of participants in the i-th test case.

Example

Input


4
4 2 5
3 1 2
3 3 10
2000000000 1 2000000000


Output


5
3
3
1999999999000000000

Note

In the first example the first participant starts at 0 and finishes at time 5. By that time the second and the third participants start, so the dissatisfaction of the first participant is 2. 

The second participant starts at time 2 and finishes at time 7. By that time the third the fourth participants start, so the dissatisfaction of the second participant is 2. 

The third participant starts at 4 and finishes at 9. By that time the fourth participant starts, so the dissatisfaction of the third participant is 1.

The fourth participant starts at 6 and finishes at 11. By time 11 everyone finishes the contest, so the dissatisfaction of the fourth participant is 0.

In the second example the first participant starts at 0 and finishes at time 2. By that time the second participants starts, and the third starts at exactly time 2. So the dissatisfaction of the first participant is 2. 

The second participant starts at time 1 and finishes at time 3. At that time the third participant is solving the contest.

import java.util.*;
import java.lang.*;
import java.io.*;

public class Main
{
     
	public static void main (String[] args) throws java.lang.Exception
	{
		FastReader sc =new FastReader();
		
	    int t=sc.nextInt();
	    
	   // int t=1;
	    
	    while(t-->0)
	    {
	        long n=sc.nextLong();
	        long x=sc.nextLong();
	        long time=sc.nextLong();
	        
	        long z = time/x;
	        if(n<z)
	        {
	            System.out.println((n-1)*n/2);
	        }
	        else
	        {
	            long ans = z*n;
	            ans-=(z*(z+1)/2);
	            System.out.println(ans);
	        }
	    }
	   
	    
	}
	
	
	
	
	static class FastReader {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(
                new InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt() { return Integer.parseInt(next()); }
 
        long nextLong() { return Long.parseLong(next()); }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
        
        float nextFloat()
        {
            return Float.parseFloat(next());
        }
 
        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        
        int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		
		long[] readArrayLong(int n) {
			long[] a=new long[n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
		
    }
    
    public static int[] radixSort2(int[] a)
	{
		int n = a.length;
		int[] c0 = new int[0x101];
		int[] c1 = new int[0x101];
		int[] c2 = new int[0x101];
		int[] c3 = new int[0x101];
		for(int v : a) {
			c0[(v&0xff)+1]++;
			c1[(v>>>8&0xff)+1]++;
			c2[(v>>>16&0xff)+1]++;
			c3[(v>>>24^0x80)+1]++;
		}
		for(int i = 0;i < 0xff;i++) {
			c0[i+1] += c0[i];
			c1[i+1] += c1[i];
			c2[i+1] += c2[i];
			c3[i+1] += c3[i];
		}
		int[] t = new int[n];
		for(int v : a)t[c0[v&0xff]++] = v;
		for(int v : t)a[c1[v>>>8&0xff]++] = v;
		for(int v : a)t[c2[v>>>16&0xff]++] = v;
		for(int v : t)a[c3[v>>>24^0x80]++] = v;
		return a;
	}
    
    static boolean isPalindrome(String str)
    {
 
        // Pointers pointing to the beginning
        // and the end of the string
        int i = 0, j = str.length() - 1;
 
        // While there are characters to compare
        while (i < j) {
 
            // If there is a mismatch
            if (str.charAt(i) != str.charAt(j))
                return false;
 
            // Increment first pointer and
            // decrement the other
            i++;
            j--;
        }
 
        // Given string is a palindrome
        return true;
    }
    
    static boolean palindrome_array(int arr[], int n)
    {
        // Initialise flag to zero.
        int flag = 0;
 
        // Loop till array size n/2.
        for (int i = 0; i <= n / 2 && n != 0; i++) {
 
            // Check if first and last element are different
            // Then set flag to 1.
            if (arr[i] != arr[n - i - 1]) {
                flag = 1;
                break;
            }
        }
 
        // If flag is set then print Not Palindrome
        // else print Palindrome.
        if (flag == 1)
            return false;
        else
            return true;
    }
    
	static boolean allElementsEqual(int[] arr,int n)
	{
	    int z=0;
	        for(int i=0;i<n-1;i++)
		    {
		        if(arr[i]==arr[i+1])
		        {
		            z++;
		        }
		    }
		    if(z==n-1)
		    {
		        return true;
		    }
		    else
		    {
		        return false;
		    }
		    
	}
	
	static boolean allElementsDistinct(int[] arr,int n)
	{
	    int z=0;
	        for(int i=0;i<n-1;i++)
		    {
		        if(arr[i]!=arr[i+1])
		        {
		            z++;
		        }
		    }
		    if(z==n-1)
		    {
		        return true;
		    }
		    else
		    {
		        return false;
		    }
		    
		    
	}
	
	public static void reverse(int[] array)
    {
  
        // Length of the array
        int n = array.length;
  
        // Swaping the first half elements with last half
        // elements
        for (int i = 0; i < n / 2; i++) {
  
            // Storing the first half elements temporarily
            int temp = array[i];
  
            // Assigning the first half to the last half
            array[i] = array[n - i - 1];
  
            // Assigning the last half to the first half
            array[n - i - 1] = temp;
        }
    }
    
    public static void reverse_Long(long[] array)
    {
  
        // Length of the array
        int n = array.length;
  
        // Swaping the first half elements with last half
        // elements
        for (int i = 0; i < n / 2; i++) {
  
            // Storing the first half elements temporarily
            long temp = array[i];
  
            // Assigning the first half to the last half
            array[i] = array[n - i - 1];
  
            // Assigning the last half to the first half
            array[n - i - 1] = temp;
        }
    }
	
	static boolean isSorted(int[] a)
    {
        for (int i = 0; i < a.length - 1; i++)
        {
            if (a[i] > a[i + 1]) {
                return false;
            }
        }
 
        return true;
    }
    
    static boolean isReverseSorted(int[] a)
    {
        for (int i = 0; i < a.length - 1; i++)
        {
            if (a[i] < a[i + 1]) {
                return false;
            }
        }
 
        return true;
    }
    
    static int[] rearrangeEvenAndOdd(int arr[], int n)
    {
        ArrayList<Integer> list = new ArrayList<>();
		    
		    for(int i=0;i<n;i++)
		    {
		        if(arr[i]%2==0)
		        {
		            list.add(arr[i]);
		        }
		    }
		    
		    for(int i=0;i<n;i++)
		    {
		        if(arr[i]%2!=0)
		        {
		            list.add(arr[i]);
		        }
		    }
		    int len = list.size();
		    int[] array = list.stream().mapToInt(i->i).toArray();
		    return array;
    }
    
    static long[] rearrangeEvenAndOddLong(long arr[], int n)
    {
        ArrayList<Long> list = new ArrayList<>();
		    
		    for(int i=0;i<n;i++)
		    {
		        if(arr[i]%2==0)
		        {
		            list.add(arr[i]);
		        }
		    }
		    
		    for(int i=0;i<n;i++)
		    {
		        if(arr[i]%2!=0)
		        {
		            list.add(arr[i]);
		        }
		    }
		    int len = list.size();
		    long[] array = list.stream().mapToLong(i->i).toArray();
		    return array;
    }
	
	
    
    static boolean isPrime(long n)
    {
 
        // Check if number is less than
        // equal to 1
        if (n <= 1)
            return false;
 
        // Check if number is 2
        else if (n == 2)
            return true;
 
        // Check if n is a multiple of 2
        else if (n % 2 == 0)
            return false;
 
        // If not, then just check the odds
        for (long i = 3; i <= Math.sqrt(n); i += 2)
        {
            if (n % i == 0)
                return false;
        }
        return true;
    }
    
    static int getSum(int n)
    {    
        int sum = 0;
          
        while (n != 0)
        {
            sum = sum + n % 10;
            n = n/10;
        }
      
    return sum;
    }
    
    static int gcd(int a, int b)
    {
      if (b == 0)
        return a;
      return gcd(b, a % b);
    }
     
    static long gcdLong(long a, long b)
    {
        if (b == 0)
        return a;
      return gcdLong(b, a % b);
    }
    
    static void swap(int[] arr, int i, int j)
    {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
	
	static int countDigit(long n)
    {
        return (int)Math.floor(Math.log10(n) + 1);
    }
	
}