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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.lang.invoke.MethodHandles;
import java.nio.file.Files;
import java.nio.file.Paths;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Objects;
import java.util.Optional;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.stream.Collectors;

public class Main {

    static class FastScanner {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        Integer[] readArrayInt(int n) {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }

    static class Pair {

        int first;

        int second;

        public Pair(int first, int second) {
            this.first = first;
            this.second = second;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }
            Pair pair = (Pair) o;
            return first == pair.first && second == pair.second;
        }

        @Override
        public int hashCode() {
            return Objects.hash(first, second);
        }
    }

    static class Equation {

        // ax+by=c;
        int a, b, c;

        public Equation(int x1, int y1, int x2, int y2) {
            int a = y2 - y1;
            int b = x1 - x2;
            int c = a * x1 + b * y1;
        }

        public Equation(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

        public boolean isPointOnLine(int x, int y) {
            return a * x + b * y == c;
        }
    }

    private static void buildGraph(HashMap<Integer, Set<Integer>> map, int first, int second) {
        Set<Integer> set = map.getOrDefault(first, new HashSet<>());
        set.add(second);
        map.put(first, set);
        set = map.getOrDefault(second, new HashSet<>());
        set.add(first);
    }

    public static void parseAndGenerate() {
    }

    public static void main(String[] args) {
        parseAndGenerate();
        try (PrintWriter out = new PrintWriter(System.out)) {
            FastScanner scanner = new FastScanner();
            int t = scanner.nextInt();
            for (int tCase = 0; tCase < t; tCase++) {
                int n = scanner.nextInt();
                int k = scanner.nextInt();
                if (k > n) {
                    out.println("NO");
                } else if (n == k) {
                    out.println("YES");
                    for (int i = 0; i < k; i++) {
                        out.print("1 ");
                    }
                    out.println();
                } else {
                    if (n % 2 == 0 && (n > 2 * (k - 1))) {
                        out.println("YES");
                        for (int i = 0; i < k - 1; i++) {
                            out.print("2 ");
                        }
                        out.print((n - 2 * (k - 1)));
                        out.println();
                        continue;
                    }
                    if ((n - k) % 2 == 0) {
                        out.println("YES");
                        for (int i = 0; i < k - 1; i++) {
                            out.print("1 ");
                        }
                        out.print((n - (k - 1)));
                        out.println();
                        continue;
                    }
                    out.println("NO");
                }
            }
        }
    }
}