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.BufferedReader;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class A {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
//        BufferedReader br = new BufferedReader(new InputStreamReader(new FileInputStream("/Users/wasim/Documents/learn/gfg/src/main/java/codeforces/contest_639/input.txt")));


        int testCase = Integer.parseInt(br.readLine());

        while (testCase-- > 0) {
            StringTokenizer st = new StringTokenizer(br.readLine());
            int n = Integer.parseInt(st.nextToken());
            int k = Integer.parseInt(st.nextToken());
            combine(n, k);
//            roundCount(m);
        }

    }

    private static void combine(int n, int k) {
        int remain = n - k +1;
        if (remain > 0 && remain %2 == 1) {
            System.out.println("YES");
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i< k-1; i++) {
                sb.append("1 ");
            }
            sb.append(remain);
            System.out.println(sb);
        } else {
            int evenRemain = n - (k - 1) * 2;
            if (evenRemain > 0 && evenRemain % 2 == 0) {
                System.out.println("YES");
                StringBuilder sb = new StringBuilder();
                for (int i = 0; i< k-1; i++) {
                    sb.append("2 ");
                }
                sb.append(evenRemain);
                System.out.println(sb);
            } else {
                System.out.println("NO");
            }
        }

    }
}