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:

for q in range(int(input())):
	n, k = map(int,input().split())
	if k > n:
		print('NO')
	elif k == n:
		print('YES')
		print('1 ' * n)
	else:
		if k % 2 == 0:
			if n % 2 == 1:
				print("NO")
			else:
				res = []
				flag = False
				N = n
				K = k
				while n > 0 and k > 0:
					res.append(2)
					n-=2
					k-=1
				if n > 0:
					res.pop()
					res.append(n + 2)
					print('YES')
					print(*res)
					flag = True
				else:
					if k == 0:
						print('YES')
						print(*res)	
						flag = True
					else:
						pass
				if flag == False:
					res = []
					n = N
					k = K
					while n > 0 and k > 0:
						res.append(1)
						n-=1
						k-=1
					if n > 0:
						res.pop()
						res.append(n + 1)
					print('YES')
					print(*res)

		else:
			if n % 2 == 1:
				res = []
				while n > 0 and k > 0:
					res.append(1)
					n-=1
					k-=1
				if n > 0:
					res.pop()
					res.append(n + 1)
				print('YES')
				print(*res)				
			else:
				res = []
				while n > 0 and k > 0:
					res.append(2)
					n-=2
					k-=1
				if n > 0:
					res.pop()
					res.append(n + 2)
					print('YES')
					print(*res)
				else:
					if k == 0:
						print('YES')
						print(*res)	
					else:
						print('NO')