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:
from collections import Counter,defaultdict,deque
#import heapq as hq
#import itertools
from operator import itemgetter
#from itertools import count, islice
#from functools import reduce
#alph = 'abcdefghijklmnopqrstuvwxyz'
#from math import factorial as fact
#a,b = [int(x) for x in input().split()]
#sarr = [x for x in input().strip().split()]
import math
import sys
input=sys.stdin.readline
#sys.setrecursionlimit(2**30)

def solve():
    n,k = [int(x) for x in input().split()]
    res = []
    if k>n:
        print('NO')
        return
    if n&1 and not k&1:
        print('NO')
        return
    if n&1^1 and k&1:
        if k*2>n:
            print('NO')
            return
        while k-1:
            res.append(2)
            n-=2
            k-=1
        print('YES')
        print(*res,n)
    else:
        while k-1:
            n-=1
            k-=1
            res.append(1)
        print('YES')
        print(*res,n)

tt = int(input())
for test in range(tt):
    solve()















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