Problem: You are given two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100). Represent the number n as the sum of k positive integers of the same parity (have the same remainder when divided by 2).

In other words, find a_1, a_2, …, a_k such that all a_i>0, n = a_1 + a_2 + … + a_k and either all a_i are even or all a_i are odd at the same time.

If such a representation does not exist, then report it.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases in the input. Next, t test cases are given, one per line.

Each test case is two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100).

Output

For each test case print:

  * YES and the required values a_i, if the answer exists (if there are several answers, print any of them); 
  * NO if the answer does not exist. 



The letters in the words YES and NO can be printed in any case.

Example

Input


8
10 3
100 4
8 7
97 2
8 8
3 10
5 3
1000000000 9


Output


YES
4 2 4
YES
55 5 5 35
NO
NO
YES
1 1 1 1 1 1 1 1
NO
YES
3 1 1
YES
111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111120

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.util.zip.Adler32;

public class B {

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int tc = sc.nextInt();
		while (tc-- > 0) {
			long n = sc.nextInt();
			long k = sc.nextInt();

			if (k % 2 == 0) {
				if (n % 2 == 1)
					pw.println("NO");
				else {
					if (k > n)
						pw.println("NO");
					else {
						pw.println("YES");
						for (int i = 0; i < k - 1; i++) {
							pw.print(1 + " ");
							
						}
						pw.println(n - (k - 1));
					}
				}
			} else {
				if (n % 2 == 0) {
					if (2 * k > n)
						pw.println("NO");
					else {
						pw.println("YES");
						for (int i = 0; i < k - 1; i++) {
							pw.print(2 + " ");

						}
						pw.println(n - (2 * (k - 1)));
					}
				} else {
					if (k > n)
						pw.println("NO");
					else {
						pw.println("YES");
						for (int i = 0; i < k - 1; i++) {
							pw.print(1 + " ");

						}
						pw.println(n - (k - 1));
					}
				}

			}
			pw.flush();
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}

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

		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();
		}
	}

}