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:
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
#      .      '                    Udit Gupta @luctivud         ,              
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
                            ##     ##  #######  # #  ######
                            ##     ##  ##   ##  ###    ##
                            ##     ##  ##    #  # #    ##
                            #########  #######  # #    ##
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

import sys
import math as mt
# sys.setrecursionlimit(10**6)

def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_array(): return list(map(int, sys.stdin.readline().strip().split()))

def printwsp(*args): return print(*args, end="")
def printsp(*args): return print(*args, end=" ")
def printchk(*args): return print(*args, end="tst, ")

MOD = int(1e9+7); BABYMOD = 998244353;
# ################################ HELPER PROGRAMS USED ###################################
# ################################## MAIN STARTS HERE #####################################
for _testcases_ in range(int(input())):
	n, k = get_ints()
	if (n % 2 == 1 and k % 2 == 0): print("NO")
	elif (k > n): print("NO")
	elif(n % 2 == 1):
		print("YES")
		rem = n
		for i in range(k):
			if i == k-1:
				print(rem)
			else:
				printsp(1)
				rem -= 1
	elif(n % 2 == 0):
		if (k % 2 == 0):
			rem = n
			print("YES")
			for i in range(k):
				if i == k-1:
					print(rem)
				else:
					printsp(1)
					rem -= 1
		else:
			if (n >= 2 * k):
				print("YES")
				rem = n
				for i in range(k):
					if i == k-1:
						print(rem)
					else:
						printsp(2)
						rem -= 2
			else: print("NO")



# #########################################################################################
'''
THE LOGIC AND APPROACH WAS DEVELOPED BY ME @luctivud.
SOME PARTS OF THE CODE HAS BEEN TAKEN FROM WEBSITES LIKE::
8
10 3
100 4
8 7
97 2
8 8
3 10
5 3
1000000000 9

(I Own the code if no link is provided here or I may have missed mentioning it)
PLEASE DO NOT PLAGIARISE.
'''