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.lang.*;
public class Main{
    static ArrayList<Long> a = new ArrayList<>();
    static boolean tryeven(long n,long k){
        long sum = 0;
        sum = (k-1)*2;
        for(int i =0;i<(k-1);i++){
            a.add((long)2);
        }
        if(sum>=n)
            return false;
        long temp = n-sum;
        a.add(temp);
        if( temp%2 == 0)
            return true;
        else
            return false;
    
    }

    static boolean tryodd(long n, long k){
        long sum = 0;
        sum = (k-1)*1;
        for(int i =0;i<(k-1);i++){
            a.add((long)1);
        }
        if(sum>=n)
            return false;
        long temp = n-sum;
        a.add(temp);
        if( temp%2 == 1)
            return true;
        else
            return false;
    }
    public static void main(String [] args){
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for(int i =0;i<t;i++){
            // ArrayList a = new ArrayList<>();
            long n = sc.nextLong();
            long k = sc.nextLong();
            int n_p = 0,k_p = 0;
            n_p = (n%2 == 0)?1:0;
            k_p = (k%2 == 0)?1:0;
            // System.out.println("NP AND KP :"+n_p+" "+k_p);
            if(n_p == 0 && k_p == 1)
                System.out.println("No");
            else if(n_p == 1 && k_p == 1){
                a.clear();
                boolean ans = tryeven(n,k);
                if(ans == true){
                    System.out.println("Yes");
                    for(int j = 0;j<a.size();j++){
                        System.out.print(a.get(j)+" ");
                    }
                    System.out.println("");
                    
                     // print yes and array values
                    
                }
                else{
                    a.clear();
                    boolean ans2 = tryodd(n,k);
                    if(ans2 == true){
                        System.out.println("Yes");
                        for(int j = 0;j<a.size();j++){
                        System.out.print(a.get(j)+" ");
                    }
                    System.out.println("");
                    }
                         // print yes and array values
                    else
                        System.out.println("No");
                }
            }
            else if(n_p == 0 && k_p == 0){
                a.clear();
                boolean ans = tryodd(n,k);
                if(ans == true){
                    System.out.println("Yes");
                    for(int j = 0;j<a.size();j++){
                        System.out.print(a.get(j)+" ");
                    }
                    System.out.println("");
                    //print array vales
                }
                else
                    System.out.println("No");
            }
            else{
                a.clear();
                boolean ans = tryeven(n,k);
                if(ans == true){
                     System.out.println("Yes");
                     for(int j = 0;j<a.size();j++){
                        System.out.print(a.get(j)+" ");
                    }
                    System.out.println("");
                }
                    
                else
                     System.out.println("No");
            }
            
        }
    }
}