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.InputStreamReader;
import java.util.*;

public class CODECHEF {
    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 (Exception 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 (Exception e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static void main(String[] args) {
        FastReader fs=new FastReader();
        int test=fs.nextInt();
        while(test-- > 0){
           long n=fs.nextLong();
           long k=fs.nextLong();

           if(k>n)
               System.out.println("NO");
           else if(k==n){
               System.out.println("YES");
               while(k-->1){
                   System.out.print(1+" ");
                   n--;
               }
               System.out.println(n);
           }else{
               //k<n
               if(k%2==0 && n%2!=0)
                   System.out.println("NO");
               else if((k%2==0 && n%2==0)||(k%2!=0 && n%2!=0)){
                   System.out.println("YES");
                   while(k-->1){
                       System.out.print(1+" ");
                       n--;
                   }
                   System.out.println(n);
               }else if(k%2!=0 && n%2==0){
                   if(k>n/2)
                       System.out.println("NO");
                   else{
                       System.out.println("YES");
                       while(k-->1){
                           System.out.print(2+" ");
                           n-=2;
                       }
                       System.out.println(n);
                   }
               }
           }
        }

    }
}