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.*;

public class Poster {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t=sc.nextInt();
		while(t-->0) {
			ArrayList<Integer>al=new ArrayList<>();
			int n = sc.nextInt();
			int k =sc.nextInt();
			if((n&1)==1&&(k&1)==0) {
				System.out.println("NO");
				System.out.println();
			}else if(k>n) {
				System.out.println("NO");
				System.out.println();
			}else if(n-k==1) {
				if(k==1) {
					System.out.println("YES");
					System.out.println(n);
				}else {
				System.out.println("NO");
				}
				System.out.println();
			}else if(n%k==0) {
				System.out.println("YES");
				for(int i=0;i<k;i++) {
					System.out.print(n/k+" ");
				}
				System.out.println();
			}else if((n&1)==1&&(k&1)==1){
				System.out.println("YES");
				for(int i=0;i<k-1;i++) {
					System.out.print(1+" ");
					
				}
				System.out.print(n-k+1);
				System.out.println();
			}else if(n==k) {
				System.out.println("YES");
				for(int i=0;i<n;i++) {
					System.out.print(1+" ");
				}
				System.out.println();
			}else if((n&1)==0&&(k&1)==0) {
				System.out.println("YES");
				for(int i=0;i<k-1;i++) {
					System.out.print(1+" ");
					
				}
				System.out.print(n-k+1);
				System.out.println();
			}else {
				if(k*2>n) {
					System.out.println("NO");
				}else {
				System.out.println("YES");
				for(int i=0;i<k-1;i++) {
					System.out.print(2+" ");
				}
				System.out.print(n-(k-1)*2);
				System.out.println();
				}
				System.out.println();
			}
		}
		
		
		
	}
	static int gcd(int a,int b) {
		if(b==0)return a;
		return gcd(b,a%b);
	}
}