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.io.*;
import java.util.*;
import java.math.*;
import java.math.BigInteger; 
//import javafx.util.*; 
public final class B
{    
	static PrintWriter out = new PrintWriter(System.out); 
	static StringBuilder ans=new StringBuilder();
	static FastReader in=new FastReader();
	static ArrayList<Integer> g[],og[];
	static long mod=(long)(1e9+7);
	static int D1[],D2[],par[];
	static boolean set[];
	static int value[];
	static long INF=Long.MAX_VALUE;
	static int val[],tot[],max[];
	static int min;
	static int dp[][][];
	static int path[][],A[];
	static char X[][];
	static int index[];
	public static void main(String args[])throws IOException
	{

		int T=i();
		outer:while(T-->0)
		{
			long N=l(),X=l(),t=l();
			long f=t/X;
			long index=f(t,X,N,f);
			//System.out.println(index);
			long s=index*f;
			long n=N-index;
			s+=(n)*(n-1)/2;
			out.println(s);
		}
		//		out.println(ans);
		out.close();
	}

	static long f(long t,long x,long N,long v)
	{
		long l=0,r=N+1;
		while(r-l>1)
		{
			long m=(l+r)/2;
			if(t+m*x<=N*x)l=m;
			else r=m;
		}
		return l;
	}

	static void f(int dp[][],int d,int A[],int par[])
	{
		if(A[d]==0)return ;
		f(dp,d+1,A,par);
		dp[0][d]=A[d]+Math.min(dp[0][d+1], dp[1][d+1]);
		if(dp[0][d+1]<dp[1][d+1])
		{
			par[d]=1;
		}
		else par[d]=2;
		dp[1][d]=dp[0][d+1];

	}
	static int [] ask(int a,int N)
	{
		System.out.println("? "+a);
		int A[]=input(N);
		return A;
	}
	static boolean isPalin(char X[])
	{
		int l=0,r=X.length-1;
		while(l<=r)
		{
			if(X[l]!=X[r])return false;
			l++;
			r--;
		}
		return true;
	}

	static boolean isSorted(int A[])
	{
		int N=A.length;
		for(int i=0; i<N-1; i++)
		{
			if(A[i]>A[i+1])return false;
		}

		return true;		
	}
	static int f1(int x,ArrayList<Integer> A)
	{
		int l=-1,r=A.size();
		while(r-l>1)
		{
			int m=(l+r)/2;
			int a=A.get(m);
			if(a<x)l=m;
			else r=m;
		}		
		return l;
	}






	static int max(int a,int b,int c)
	{
		return Math.max(a, Math.max(c, b));
	}
	static int value(char X[],char Y[])
	{
		int c=0;
		for(int i=0; i<7; i++)
		{
			if(Y[i]=='1' && X[i]=='0')return -1;
			if(X[i]=='1' && Y[i]=='0')c++;
		}
		return c;
	}
	//	static boolean isValid(int i,int j)
	//	{
	//		if(i<0 || i>=N)return false;
	//		if(j<0 || j>=M)return false;
	//		return true;
	//	}

	static long fact(long N)
	{
		long num=1L;
		while(N>=1)
		{
			num=((num%mod)*(N%mod))%mod;
			N--;
		}
		return num;
	}
	static boolean reverse(long A[],int l,int r)
	{
		while(l<r)
		{
			long t=A[l];
			A[l]=A[r];
			A[r]=t;
			l++;
			r--;
		}
		if(isSorted(A))return true;
		else return false;
	}
	static boolean isSorted(long A[])
	{
		for(int i=1; i<A.length; i++)if(A[i]<A[i-1])return false;
		return true;
	}
	static boolean isPalindrome(char X[],int l,int r)
	{
		while(l<r)
		{
			if(X[l]!=X[r])return false;
			l++; r--;
		}
		return true;
	}

	static long min(long a,long b,long c)
	{
		return Math.min(a, Math.min(c, b));
	}

	static void print(int a)
	{
		System.out.println("! "+a);
	}
	static int find(int a)
	{
		if(par[a]<0)return a;
		return par[a]=find(par[a]);
	}
	static void union(int a,int b)
	{
		a=find(a);
		b=find(b);
		if(a!=b)
		{
			par[a]+=par[b]; //transfers the size
			par[b]=a;       //changes the parent
		}
	}
	static void swap(char A[],int a,int b)
	{
		char ch=A[a];
		A[a]=A[b];
		A[b]=ch;
	}

	static void sort(long[] a) //check for long
	{
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
	static void setGraph(int N)
	{
		g=new ArrayList[N+1];		
		og=new ArrayList[N+1];

		val=new int[N+1];
		for(int i=0; i<=N; i++)
		{
			og[i]=new ArrayList<Integer>();			
			g[i]=new ArrayList<Integer>();
		}
	}

	static  long pow(long a,long b)
	{
		long mod=1000000007;
		long pow=1;
		long x=a;
		while(b!=0)
		{
			if((b&1)!=0)pow=(pow*x)%mod;
			x=(x*x)%mod;
			b/=2;
		}
		return pow;
	}
	static long toggleBits(long x)//one's complement || Toggle bits
	{
		int n=(int)(Math.floor(Math.log(x)/Math.log(2)))+1;

		return ((1<<n)-1)^x;
	}
	static int countBits(long a)
	{
		return (int)(Math.log(a)/Math.log(2)+1);
	}
	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
	static boolean isPrime(long N)
	{
		if (N<=1)  return false; 
		if (N<=3)  return true; 
		if (N%2 == 0 || N%3 == 0) return false; 
		for (int i=5; i*i<=N; i=i+6) 
			if (N%i == 0 || N%(i+2) == 0) 
				return false; 
		return true; 
	}
	static long GCD(long a,long b) 
	{
		if(b==0)
		{
			return a;
		}
		else return GCD(b,a%b );
	}

	//Debugging Functions Starts

	static void print(char A[])
	{
		for(char c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(boolean A[])
	{
		for(boolean c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(int A[])
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();	
	}
	static void print(long A[])
	{
		for(long i:A)System.out.print(i+ " ");
		System.out.println();

	}
	static void print(ArrayList<Integer> A)
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();
	}

	//Debugging Functions END
	//----------------------
	//IO FUNCTIONS STARTS
	static HashMap<Integer,Integer> Hash(int A[])
	{
		HashMap<Integer,Integer> mp=new HashMap<>();
		for(int a:A)
		{
			int f=mp.getOrDefault(a,0)+1;
			mp.put(a, f);
		}
		return mp;
	}
	static int i()
	{
		return in.nextInt();
	}

	static long l()
	{
		return in.nextLong();
	}

	static int[] input(int N){
		int A[]=new int[N];
		for(int i=0; i<N; i++)
		{
			A[i]=in.nextInt();
		}
		return A;
	}

	static long[] inputLong(int N)     {
		long A[]=new long[N];
		for(int i=0; i<A.length; i++)A[i]=in.nextLong();
		return A;
	}

	//IO FUNCTIONS END

}

class node implements Comparable<node>
{
	int par,a;
	node(int par,int a)
	{
		this.par=par;
		this.a=a;
	}
	public int compareTo(node x)
	{
		return this.par-x.par;
	}
}

//Code For FastReader
//Code For FastReader
//Code For FastReader
//Code For FastReader
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());
	}
	//gey
	double nextDouble()
	{
		return Double.parseDouble(next());
	}

	String nextLine()
	{
		String str="";
		try
		{
			str=br.readLine();
		}
		catch (IOException e)
		{
			e.printStackTrace();
		}
		return str;
	}

}