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 B_Same_Parity_Summands {

    static 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;
        }
    }

    public static void main(String[] args) {
        FastReader scan = new FastReader();
        int t = scan.nextInt();
        while (t-- > 0) {
            int n = scan.nextInt();
            int k = scan.nextInt();

            if (k > n) {
                System.out.println("NO");
                continue;
            }

            if (k == 1) {
                System.out.println("YES");
                System.out.println(n);
                continue;
            }

            if (n == k) {
                System.out.println("YES");
                for (int i = 0; i < n; i++) {
                    System.out.print("1 ");
                }
                System.out.println();
                continue;
            }

            if (n % k == 0) {
                System.out.println("YES");
                for (int i = 0; i < k; i++) {
                    System.out.print(n / k + " ");
                }
                System.out.println();
                continue;
            }

            if ((n & 1) == 1 && (k & 1) == 1) {
                int start = 0;
                System.out.println("YES");
                while (k-- > 1) {
                    start++;
                    System.out.print("1 ");
                }
                System.out.println(n - start);

            } else if ((n & 1) == 1 && (k & 1) != 1) {
                System.out.println("NO");
            } else if (2 * (k - 1) >= n) {
                if (((n - (k - 1)) & 1) == 1) {
                    System.out.println("YES");
                    int x = k;
                    while (x-- > 1) {
                        System.out.print("1 ");
                    }
                    System.out.println(n - (k - 1));
                } else {
                    System.out.println("NO");
                }
            } else {
                int start = 0;
                System.out.println("YES");
                while (k-- > 1) {
                    start += 2;
                    System.out.print("2 ");
                }
                System.out.println(n - start);
            }

            // if (((n - (k - 1)) & 1) == 1) {
            // System.out.println("YES");
            // int x = k;
            // while (x-- > 1) {
            // System.out.print("1 ");
            // }
            // System.out.println(n - (k - 1));
            // } else {

            // }

        }
    }
}