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:


/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.StringTokenizer;

/**
 *
 * @author is2ac
 */
public class B_CF {

    public static void main(String[] args) {
        FastScanner56 fs = new FastScanner56();
        PrintWriter pw = new PrintWriter(System.out);
        int t = fs.ni();
        //int t = 1;
        //Boolean[][][] dp = new Boolean[101][101][10001];
        for (int tc = 0; tc < t; tc++) {
            int n = fs.ni();
            int k = fs.ni();
            if (n%2==1 && k%2==0) {
                pw.println("NO");
                continue;
            }
            StringBuilder sb = new StringBuilder();
            if (n%2==k%2) {
                if (k>n) {
                    pw.println("NO");
                    continue;
                }
                sb.append(n-k+1);
                sb.append(" ");
                for (int i = 1; i < k; i++) {
                    sb.append(1 + " ");
                }
            } else if (n%2==0) {
                if (k*2>n) {
                    pw.println("NO");
                    continue;
                }
                sb.append(n-(k-1)*2);
                sb.append(" ");
                for (int i = 1; i < k; i++) {
                    sb.append(2 + " ");
                }
            }
            pw.println("YES");
            pw.println(sb);
        }
        pw.close();
    }

    static boolean isp(int x) {
        int y = (int) Math.sqrt(x);
        if(Math.pow(y,2) == x) return true;
        return false;
    }
}

class FastScanner56 {

    BufferedReader br;
    StringTokenizer st;

    public FastScanner56() {
        br = new BufferedReader(new InputStreamReader(System.in), 32768);
        st = null;
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int ni() {
        return Integer.parseInt(next());
    }

    int[] intArray(int N) {
        int[] ret = new int[N];
        for (int i = 0; i < N; i++) {
            ret[i] = ni();
        }
        return ret;
    }

    long nl() {
        return Long.parseLong(next());
    }

    long[] longArray(int N) {
        long[] ret = new long[N];
        for (int i = 0; i < N; i++) {
            ret[i] = nl();
        }
        return ret;
    }

    double nd() {
        return Double.parseDouble(next());
    }

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