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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Same_Parity_Summ {
    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());
        }

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

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
    public static void main(String[] args) {
        FastReader in = new FastReader();
        int t = in.nextInt();
        StringBuilder sb = new StringBuilder();
        while(t-- > 0){
            long n = in.nextLong();
            long k = in.nextLong();

            if(n % 2 == 0){
                   if(k % 2 == 0){
                        long x = n - (k - 1);
                        if(x > 0){
                            sb.append("YES"+"\n");
                            for(int i = 1; i < k; i++){
                                sb.append(1+" ");
                            }
                            sb.append(x+"\n");
                        }else{
                            sb.append("NO"+"\n");
                        }
                   }else{
                       long x = n - 2*(k - 1);
                       if(x > 0){
                           sb.append("YES"+"\n");
                           for(int i = 1; i < k; i++){
                               sb.append("2"+" ");
                           }
                           sb.append(x+"\n");
                       }else{
                           sb.append("NO"+"\n");
                       }
                   }
            }else{
                if(k % 2 == 0){
                    sb.append("NO"+"\n");
                }else{
                    long x = n - (k - 1);
                    if(x > 0){
                        sb.append("YES"+"\n");
                        for(int i = 1; i < k; i++){
                            sb.append(1+" ");
                        }
                        sb.append(x+"\n");
                    }else{
                        sb.append("NO"+"\n");
                    }
                }
            }
        }
        System.out.println(sb);
    }
}