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 createSumm(n,k):
	if n<k:
		return 0
	elif n%2==1 and k==1:
		l = []
		l.append(n)
		return l
	else:
		l = []
		c = k-1
		if (n-2*c)%2==0 and (n-2*c)>0:
			for i in range(c):
				l.append(2)
			l.append(n-2*c)
			return l
		if (n-c)%2!=0 and (n-c)>0:
			for i in range(c):
				l.append(1)
			l.append(n-c)
			return l
			
		else:
			return 0

def  outputRes(a_list):
	for i in a_list:
		if i==0:
			print("NO")
		else:
			print("YES")
			for j in i:
				print(j,end=" ")
			print(end="\n")

def inputVal():
	t = int(input(""))
	a_list=[]
	for i in range(t):
		vals = input("").split(" ")
		n = int(vals[0])
		k = int(vals[1])
		a_list.append(createSumm(n,k))
	outputRes(a_list)


inputVal()