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.io.*;
public class B
{
    static BufferedReader br;
    static BufferedWriter bw;
    static void solve()throws Exception
    {
        int nk[] = Arrays.stream(br.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
        int n = nk[0];
        int k = nk[1];
        if(n<k)
        bw.write("NO");
        else if(n==k)
        {
            bw.write("YES");    
            bw.newLine();
            for(int i=0;i<k;i++)
                bw.write("1 "); 
        }
        else
        {
            if(n%2==1 && k%2==0)
            bw.write("NO");
            else if(n%2==0 && n<2*k)
            {
                if(k%2!=0)
                {
                    bw.write("NO");
                }else{
                bw.write("YES");
                bw.newLine();
                int x = 0;
                while(k!=1)
                {
                    x++;
                    bw.write("1 ");
                    k--;
                }
                bw.write(Integer.toString(n-x));
            }
            }
            else
            {
                bw.write("YES");
                bw.newLine();
                if(n%2==1)
                {
                    int x = 0;
                    while(k!=1)
                    {
                        x++;
                        bw.write("1 ");
                        k--;
                    }
                    bw.write(Integer.toString(n-x));
                }
                else
                {
                    int x = 0;
                    while(k!=1)
                    {
                        x++;
                        bw.write("2 ");
                        k--;
                    }
                    bw.write(Integer.toString(n-2*x));
                }
            }
        }
        bw.newLine();
    }
    public static void main(String []args)throws Exception
    {
        br = new BufferedReader(new InputStreamReader(System.in));
        bw = new BufferedWriter(new OutputStreamWriter(System.out));
        int t = Integer.parseInt(br.readLine());
        for(int i=0;i<t;i++)
        {
            solve();
        }
        bw.close();
        br.close();
    }
}