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.*;
import java.util.*;


public class Ladder {
    public static void main(String[] args) throws IOException {
        //BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
 // /*      //Scanner scanner=new Scanner(System.in);
        Reader scanner=new Reader();
        int n=scanner.nextInt();
        for (int i = 0; i <n ; i++) {
            int a=scanner.nextInt();
            int k=scanner.nextInt();
            if (k>a || (a%2!=0 && k%2==0)){
                System.out.println("NO");
                continue;
            }
            if (a%2!=0){
                int t=a-(k-1);
                System.out.println("YES");
                for (int j = 0; j < k-1; j++) {
                    System.out.print(1+" ");
                }
                System.out.println(t);
            }
            if (a%2==0 && k<=(a/2)){
                int t=a-(k-1)*2;
                System.out.println("YES");
                for (int j = 0; j < k-1; j++) {
                    System.out.print(2+" ");
                }
                System.out.println(t);
            }
            if (a%2==0 && k>(a/2) && k%2==0){
                int t=a-(k-1);
                System.out.println("YES");
                for (int j = 0; j < k-1; j++) {
                    System.out.print(1+" ");
                }
                System.out.println(t);
            }
            if (a%2==0 && k>(a/2) && k%2!=0){

                System.out.println("NO");

            }


        }

    }

}


class Reader {
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader() {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException {
        din = new DataInputStream(new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String readLine() throws IOException {
        byte[] buf = new byte[64];
        int cnt = 0, c;
        while ((c = read()) != -1) {
            if (c == '\n') break;
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }

    public int nextInt() throws IOException {
        int ret = 0;
        byte c = read();
        while (c <= ' ') c = read();
        boolean neg = (c == '-');
        if (neg) c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg) return -ret;
        return ret;
    }

    public long nextLong() throws IOException {
        long ret = 0;
        byte c = read();
        while (c <= ' ') c = read();
        boolean neg = (c == '-');
        if (neg) c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg) return -ret;
        return ret;
    }

    public double nextDouble() throws IOException {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ') c = read();
        boolean neg = (c == '-');
        if (neg) c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (c == '.') while ((c = read()) >= '0' && c <= '9') ret += (c - '0') / (div *= 10);
        if (neg) return -ret;
        return ret;
    }

    private void fillBuffer() throws IOException {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1) buffer[0] = -1;
    }

    private byte read() throws IOException {
        if (bufferPointer == bytesRead) fillBuffer();
        return buffer[bufferPointer++];
    }

    public void close() throws IOException {
        if (din == null) return;
        din.close();
    }
}