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:
//package codeforces.Div4.D20200518;

import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.Arrays;

/**
 * created by jieshu.wang on 2020/5/16 22:18.
 */
public class B {

    public static void main(String[] args) throws Exception {
        BufferInput input = new BufferInput();
        int t = input.nextInt();
        while (t-- > 0) {
            int n = input.nextInt(), k = input.nextInt();
            int even = n - (k - 1) * 1, odd = n - (k - 1) * 2;
            if (even > 0 && even % 2 == 1) {
                System.out.println("YES");
                for (int i = 0; i < k - 1; i++) {
                    System.out.print("1" + " ");
                }
                System.out.println(even);
            } else if (odd > 0 && odd % 2 == 0) {
                System.out.println("YES");
                for (int i = 0; i < k - 1; i++) {
                    System.out.print("2" + " ");
                }
                System.out.println(odd);
            } else {
                System.out.println("NO");
            }
        }
    }

    static class Node {
        int key;
        int value;

        public Node(int key, int value) {
            this.key = key;
            this.value = value;
        }

        public int getKey() {
            return key;
        }

        public int getValue() {
            return value;
        }

        public void setValue(int value) {
            this.value = value;
        }
    }


    static class BufferInput {

        final private int BUFFER_SIZE = 1 << 16;

        private DataInputStream din;

        private byte[] buffer;

        private int bufferPointer, bytesRead;

        public BufferInput() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public BufferInput(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64];
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public String nextString() throws IOException{

            byte c = read();
            while(Character.isWhitespace(c)){
                c = read();
            }

            StringBuilder builder = new StringBuilder();
            builder.append((char)c);
            c = read();
            while(!Character.isWhitespace(c)){
                builder.append((char)c);
                c = read();
            }

            return builder.toString();
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public int[] nextIntArray(int n) throws IOException {
            int arr[] = new int[n];
            for(int i = 0; i < n; i++){
                arr[i] = nextInt();
            }
            return arr;
        }
        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public long[] nextLongArray(int n) throws IOException {
            long arr[] = new long[n];
            for(int i = 0; i < n; i++){
                arr[i] = nextLong();
            }
            return arr;
        }

        public char nextChar() throws IOException{
            byte c = read();
            while(Character.isWhitespace(c)){
                c = read();
            }
            return (char) c;
        }
        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }
        public double[] nextDoubleArray(int n) throws IOException {
            double arr[] = new double[n];
            for(int i = 0; i < n; i++){
                arr[i] = nextDouble();
            }
            return arr;
        }
        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }
}