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.util.*;
import java.lang.*;
import java.io.*;
public class SameParitySummands {
	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());
        }

        String nextLine() {
            String str = "";
            try{
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
       
    }
		
		
	public static void main(String args[]) {
		FastReader sc = new FastReader();
		
		int t = sc.nextInt();
		
		while(t-- > 0) {
			int n = sc.nextInt(),  m = sc.nextInt();
			StringBuilder sb = new StringBuilder();
			if(n%2 == 1) {
				
				if(m%2 == 1) {
					long sum = 0;
					
					for(int i=0;i<m-1;i++) {
						sb.append("1 ");
						sum++;
					}
					if(sum >= n) {
						System.out.println("NO");
						continue;
					}
					sb.append(n-sum);
					System.out.println("YES\n"+sb.toString());
				}
				else {
					System.out.println("NO");
				}
			}
			
			else {
				if(m%2 == 1) {
					long sum = 0;
					for(int i = 0; i < m - 1;i++) {
						sb.append("2 ");
						sum += 2;
					}
					if(sum >= n) {
						System.out.println("NO");
						continue;
					}
					sb.append(n-sum);
					System.out.println("YES\n"+sb.toString());
				}
				else {
					long sum = 0; 
					for(int i=0;i<m-1;i++) {
						sb.append("1 ");
						sum++;
					}
					if(sum >= n) {
						System.out.println("NO");
						continue;
					}
					sb.append(n-sum);
					System.out.println("YES\n"+sb.toString());
				}
			}
		}
		}
}