Problem: We have a secret array. You don't know this array and you have to restore it. However, you know some facts about this array:

  * The array consists of n distinct positive (greater than 0) integers. 
  * The array contains two elements x and y (these elements are known for you) such that x < y. 
  * If you sort the array in increasing order (such that a_1 < a_2 < … < a_n), differences between all adjacent (consecutive) elements are equal (i.e. a_2 - a_1 = a_3 - a_2 = … = a_n - a_{n-1}). 



It can be proven that such an array always exists under the constraints given below.

Among all possible arrays that satisfy the given conditions, we ask you to restore one which has the minimum possible maximum element. In other words, you have to minimize max(a_1, a_2, ..., a_n).

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.

The only line of the test case contains three integers n, x and y (2 ≤ n ≤ 50; 1 ≤ x < y ≤ 50) — the length of the array and two elements that are present in the array, respectively.

Output

For each test case, print the answer: n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the i-th element of the required array. If there are several answers, you can print any (it also means that the order of elements doesn't matter).

It can be proven that such an array always exists under the given constraints.

Example

Input


5
2 1 49
5 20 50
6 20 50
5 3 8
9 13 22


Output


1 49 
20 40 30 50 10
26 32 20 38 44 50 
8 23 18 13 3 
1 10 13 4 19 22 25 16 7 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class A {

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int q = sc.nextInt();
		while (q-- > 0) {
			int n=sc.nextInt();
			int x=sc.nextInt();
			int y=sc.nextInt();
			int max=2000000;
			int dif=0;
			for (int i = 0; i < n; i++) {
				for (int j = i+1; j < n; j++) {
					if((y-x)%(j-i)!=0)
						continue;
					int d=(y-x)/(j-i);
					if(x-(i*d)<=0)
						continue;
					if(max>y+(n-j-1)*d) {
						dif=d;
						max=y+(n-j-1)*d;
					}
				}
			}
			for (int i = 0; i < n; i++) {
				System.out.print(max-(i*dif)+" ");
			}
			System.out.println();
		}
		pw.flush();
	}

	///////////////////////////////////////////////////////////////////////////////////////////
	static class tri {
		int x, y, z;

		public tri(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}

	}

	static class pair implements Comparable<pair> {
		int x, y;

		pair(int s, int d) {
			x = s;
			y = d;
		}

		@Override
		public int compareTo(pair p) {
			return (x == p.x && y == p.y) ? 0 : 1;
		}

		@Override
		public String toString() {
			return x + " " + y;

		}

	}

	static long mod(long ans, int mod) {
		return (ans % mod + mod) % mod;
	}

	static long gcd(long a, long b) {
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}

	static long lcm(long a, long b) {
		return (a * b) / gcd(a, b);
	}

	public static int log(int n, int base) {
		int ans = 0;
		while (n + 1 > base) {
			ans++;
			n /= base;
		}
		return ans;
	}

	static long pow(long b, long e) {
		long ans = 1;
		while (e > 0) {
			if ((e & 1) == 1)
				ans = ((ans * 1l * b));
			e >>= 1;
			{

			}
			b = ((b * 1l * b));
		}
		return ans;
	}

	static int powmod(int b, long e, int mod) {
		int ans = 1;
		b %= mod;
		while (e > 0) {
			if ((e & 1) == 1)
				ans = (int) ((ans * 1l * b) % mod);
			e >>= 1;
			b = (int) ((b * 1l * b) % mod);
		}
		return ans;
	}

	static int ceil(int a, int b) {
		int ans = a / b;
		return a % b == 0 ? ans : ans + 1;
	}

	static long ceil(long a, long b) {
		long ans = a / b;
		return a % b == 0 ? ans : ans + 1;
	}

	static HashMap<Integer, Integer> compress(int a[]) {
		TreeSet<Integer> ts = new TreeSet<>();
		HashMap<Integer, Integer> hm = new HashMap<>();
		for (int x : a)
			ts.add(x);
		for (int x : ts) {
			hm.put(x, hm.size() + 1);
		}
		return hm;
	}

	// Returns nCr % p
	static int C[];

	static int nCrModp(int n, int r, int p) {
		if (r > n - r)
			r = n - r;
		if (C[r] != 0)
			return C[r];
		// The array C is going to store last
		// row of pascal triangle at the end.
		// And last entry of last row is nCr

		C[0] = 1; // Top row of Pascal Triangle

		// One by constructs remaining rows of Pascal
		// Triangle from top to bottom
		for (int i = 1; i <= n; i++) {

			// Fill entries of current row using previous
			// row values
			for (int j = Math.min(i, r); j > 0; j--)

				// nCj = (n-1)Cj + (n-1)C(j-1);
				C[j] = (C[j] + C[j - 1]) % p;
		}
		return C[r];
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public int[] intArr(int n) throws IOException {
			int a[] = new int[n];
			for (int i = 0; i < a.length; i++) {
				a[i] = nextInt();
			}
			return a;
		}

		public long[] longArr(int n) throws IOException {
			long a[] = new long[n];
			for (int i = 0; i < a.length; i++) {
				a[i] = nextLong();
			}
			return a;
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}

	public static void shuffle(Integer[] x2) {
		int n = x2.length;
		for (int i = 0; i < n; i++) {
			int r = i + (int) (Math.random() * (n - i));
			int tmp = x2[i];
			x2[i] = x2[r];
			x2[r] = tmp;
		}
	}

}