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:
t = int(input(""))
for i in range(t):
	s = input("")
	L = s.split(" ")
	n,k = int(L[0]),int(L[1])
	if (k>n):
		print ("NO")
	else:
		if (n%2==0):
			if (k>n/2 and k%2==0):
				print ("YES")
				L = []
				for j in range(k-1):
					L.append(1)
				L.append(n-(k-1))
				for p in L:
					print (p,end=" ")
				print ("")
			elif (k<=n/2):
				print ("YES")
				L = []
				for j in range(k-1):
					L.append(2)
				L.append(n-2*(k-1))
				for p in L:
					print (p,end=" ")
				print ("")

			else:
				print ("NO")
		else:
			if (k%2==0):
				print ("NO")
			else:
				print ("YES")
				L = []
				for j in range(k-1):
					L.append(1)
				L.append(n-(k-1))
				for p in L:
					print (p,end=" ")
				print ("")