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.io.PrintWriter;
import java.util.*;
import java.util.StringTokenizer;

public class Codeforces {
    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;
        }
    }

    static FastReader s = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);

    private static int[] rai(int n) {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
        }
        return arr;
    }

    private static long[] ral(int n) {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextLong();
        }
        return arr;
    }

    private static int ri() {
        return s.nextInt();
    }

    private static long rl() {
        return s.nextLong();
    }

    private static String rs() {
        return s.next();
    }

    public static void main(String[] args) {
        int t=ri();
        StringBuilder ans=new StringBuilder();
        while(t-->0)
        {
            int n=ri();
            int k=ri();
            if((n&1)==1 && (k&1)==0)
            {
                ans.append("No\n");
                continue;
            }
            if(((n&1)==1 && (k&1)==1) || ((n&1)==0 && (k&1)==0))
            {
                StringBuilder mid=new StringBuilder();
                while(k>1 && n>0)
                {
                    mid.append("1 ");
                    k--;
                    n--;
                }
                if(n>0) {
                    ans.append("YES\n");
                    mid.append(n).append("\n");
                    ans.append(mid.toString());
                }
                else
                {
                    ans.append("No\n");
                }
            }
            else if(((n&1)==0 && (k&1)==1))
            {
                StringBuilder mid=new StringBuilder();
                while(k>1 && n>0)
                {
                    mid.append("2 ");
                    k--;
                    n-=2;
                }
                if(n>0) {
                    ans.append("YES\n");
                    mid.append(n).append("\n");
                    ans.append(mid.toString());
                }
                else
                {
                    ans.append("No\n");
                }
            }
        }
        out.print(ans.toString());
        out.flush();
    }
}
class Point
{
    int y,change;

    public Point(int y, int change) {
        this.y = y;
        this.change = change;
    }
}