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:
def test_1(n,k):
	rem = n - (k-1) * 1
	if(rem>0):
		return ['1']*(k-1)+[str(rem)]
	else:
		return -1

def test_2(n,k):
	rem = n - (k-1) * 2
	if(rem>0):
		return ['2']*(k-1)+[str(rem)]
	else:
		return -1	
def is_even(x):
	return x%2==0

def is_odd(x):
	return x%2!=0


t = int(input())
for tt in range(t):
	nk = input().split()
	n = int(nk[0])
	k = int(nk[1])

	if(is_even(n) and is_even(k)):
		tmp = test_1(n,k)
	elif(is_even(n) and is_odd(k)):
		tmp = test_2(n,k)
	elif(is_odd(n) and is_odd(k)):
		tmp = test_1(n,k)
	else:
		tmp = -1
	if(tmp==-1):
		print("NO")
	else:
		print("YES")
		print(" ".join(tmp))