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 _ in range(int(input())):
	n, k =map(int, input().split())
	lst = []
	r = n%k
	if(n < k):
		print("NO")
	elif(r == 0):
		print("YES")
		for i in range(k):
			if(i == k-1):
				print(int(n/k))
			else:
				print(int(n/k), end=" ")
	elif(r%2 == 0):
		print("YES")
		for i in range(k):	
			if(r != 0):
				if(i == k-1):
					print(int(n//k)+2)
					r -= 2
				else:
					print(int(n//k)+2, end=" ")
					r -= 2
			else:
				if(i == k-1):
					print(int(n//k))
				else:
					print(int(n//k), end=" ")
	else:
		if(r%2 == 1):
			if((k-1)%2 == 0 and n//k > 1):
				print("YES")
				lmt = (r-1)/2
				for i in range(k):
					if(i < lmt):
						lst.append(int(n//k)+2)
					else:
						lst.append(int(n//k))
				for i in range(k):
					if(i%2 == 0):
						if(i == k-1):
							print(lst[i]+1)
						else:
							print(lst[i]+1, end=" ")
					else:
						if(i == k-1):
							print(lst[i]-1)
						else:
							print(lst[i]-1, end=" ")
			else:
				print("NO")


# if(i == k-1):
# 						print(n//k+1, end=" ")
# 					elif(r != 0):
# 						if(i%2 == 0):
# 							print(n//k+1, end=" ")
# 							r -= 2
# 						else:
# 							print(n//k+3, end=" ")
# 							r -= 2
# 					else:
# 						if(r == 0):
# 							if(i%2 == 0):
# 								print(n//k-1, end=" ")
# 							else:
# 								print(n//k+1, end=" ")