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 PYTHON3):

Solution:
# -*- coding: utf-8 -*-
"""Untitled57.ipynb

Automatically generated by Colaboratory.

Original file is located at
    https://colab.research.google.com/drive/176Roy3CJpdWsShDvUzRgaAljeiyTL_Yk
"""

for _ in range(int(input())):
  n,m=input().split()
  n=int(n)
  m=int(m)
  if n%2==0 and m%2!=0:
    if m*2<=n:
      print('YES')
      print(n-(m-1)*2,end=' ')
      for i in range(m-1):
        print(2,end=' ')
    else:
      print('NO')
  elif n%2==0 and m%2==0:
    if m*1<=n:
      print('YES')
      print(n-m+1,end=' ')
      for i in range(m-1):
        print(1,end=' ')
    elif m*2<=n:
      print('YES')
      print(n-(m-1)*2,end=' ')
      for i in range(m-1):
        print(2,end=' ')
    else:
      print('NO')
  elif n%2!=0 and m%2==0:
    print('NO')
  else:
    if m*1<=n:
      print('YES')
      print(n-m+1,end=' ')
      for i in range(m-1):
        print(1,end=' ')
    else:
      print('NO')
  print()