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:
import sys 
try:
	sys.stdin = open('Input.txt', 'r') 
	sys.stdout = open('Output.txt', 'w')
except:
	pass

input = sys.stdin.readline

for testCases in range(int(input())):
	m,k = map(int,input().split())
	if (m-k+1)%2==1 and (m-k+1)>0:
		print("YES")
		ans = [1]*k
		ans[-1] = m-k+1
		print(*ans,sep=" ")
		continue
	elif (m-(2*(k-1)))%2==0 and (m-(2*(k-1)))>0:
		print("YES")
		ans = [2]*k
		ans[-1] = m-(2*(k-1))
		print(*ans,sep=" ")
		continue
	print("NO")