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 Main{
    //
    public static void nl(Object o){System.out.println(o);}
    public static void l(Object o){System.out.print(o);}
    public static void arp(int[] o){for(int i=0;i<o.length;i++) System.out.print(o[i]+" ");}
    public static void arpnl(int[] o){for(int i=0;i<o.length;i++) System.out.println(o[i]);}
    //
    static int MOD=1000000007;
    //
    public static void main(String[] args) throws IOException{
        // long sttm=System.currentTimeMillis();
        FastReader sc=new FastReader();
        OutputStream out=new BufferedOutputStream(System.out);
        int t=sc.nextInt();
        while(t-->0){
            int n=sc.nextInt(),k=sc.nextInt();
            if(k%2==0){
                if(n%2==0){
                    if(n-(k-1)>0){
                        nl("YES");
                        for(int i=0;i<k-1;i++){
                            l("1 ");
                        }
                        l(n-(k-1));
                    }
                    else{
                        l("NO");
                    }
                }
                else{
                    l("NO");
                }
            }
            else{
                if(n%2==0){
                    if(n-(2*k-2)>0){
                        nl("YES");
                        for(int i=0;i<k-1;i++){
                            l("2 ");
                        }
                        l(n-(2*k-2));
                    }
                    else{
                        l("NO");
                    }
                }
                else{
                    if(n-(k-1)>0){
                        nl("YES");
                        for(int i=0;i<k-1;i++){
                            l("1 ");
                        }
                        l(n-(k-1));
                    }
                    else{
                        l("NO");
                    }
                }
            }
            nl("");
        }
        out.flush();
    }


    // public static String decToBin(long val){
    //     String res="";
    //     while(val>0){
    //         long rem=val%2;val/=2;
    //         // res+=Integer.t
    //     }
    //     return res;
    // }

    public static boolean dfsCycle(ArrayList<Integer>[] arrl,int[] vis,int st,int pr){
        vis[st]=1;
        int cupr=st;
        for(int elm:arrl[st]){
            if(vis[elm]==1 && elm!=pr){
                return true;
            }
            else if(vis[elm]==0 && dfsCycle(arrl, vis, elm, cupr)){
                return true;
            }
        }
        vis[st]=2;
        return false;
    }



    public static long powMOD(long n,long k){                 //n-pow(k)
        if(k==1){
            return n%MOD;
        }
        if(k==0){
            return 1;
        }
        long val=pow(n,k/2)%MOD;
        if(k%2==0)return ((val%MOD)*(val%MOD))%MOD;
        else return (((val*val)%MOD)*n)%MOD;
    }

    public static long pow(long n,long k){                 //n-pow(k)
        if(k==1){
            return n;
        }
        if(k==0){
            return 1;
        }
        long val=pow(n,k/2);
        if(k%2==0)return ((val)*(val));
        else return (((val*val))*n);
    }


    public static HashMap<Integer,Integer> lcm(int num){
        ArrayList<Integer> arrl=new ArrayList<Integer>();
        HashMap<Integer,Integer> map=new HashMap<Integer,Integer>();
        while(num%2==0){

            if(!map.containsKey(2)){
                arrl.add(2);
                map.put(2, 1);
            }
            else{
                map.put(2,map.get(2)+1);
            }
            num/=2;
        }
        for(int i=3;i*i<=num;i+=2){
            while(num%i==0){
                if(!map.containsKey(i)){
                    arrl.add(i);
                    map.put(i, 1);
                }
                else{
                    map.put(i,map.get(i)+1);
                }
                num/=i;
            }
        }
        if(num>2){
            if(!map.containsKey(num)){
                arrl.add(num);
                map.put(num, 1);
            }
            else{
                map.put(num,map.get(num)+1);
            }
        }
        return map;
    }


    static long m=998244353l;
    static long modInverse(long a,long m)
    {
        long m0 = m;
        long y = 0l, x = 1l;

        if (m == 1)
            return 0l;

        while (a > 1)
        {

            long q = a / m;

            long t = m;

            m = a % m;
            a = t;
            t = y;

            y = x - q * y;
            x = t;
        }
        if (x < 0)
            x += m0;

        return x;
    }


    public static int num_fact(int num){
        ArrayList<Integer> arr=new ArrayList<Integer>();
        int cnt=0;
        for(int i=1;i*i<=num;i++){
            if(num%i==0){
                if(i*i==num){
                    cnt+=1;
                }
                else{
                    cnt+=2;
                }
            }
        }
        return cnt;
    }


    public static void sort_inc(int[][] arr,int col){        //change dimention if req
        Arrays.sort(arr, new Comparator<int[]>() {
            public int compare(final int[] entry1,final int[] entry2) {
                if (entry1[col] > entry2[col])              //this is for inc
                    return 1;
                else if(entry1[col]==entry2[col])
                    return 0;
                else
                    return -1;
            }
        });
    }


    public static boolean prime(int n){
        for(int i=2;i*i<=n;i++){
            if(n%i==0){
                return false;
            }
        }
        return true;
    }


    static long gcd(long a, long b)
	{
	if (b == 0)
		return a;
	return gcd(b, a % b);
    }

    public static long lcmOfTwo(int a,int b){
        return a*b/gcd(a,b);
    }

}


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;
    }
}