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:
"""
~~ Author : Bhaskar
~~ Dated : 10~06~2020
"""

import sys
from bisect import *
from math import floor,sqrt,ceil,factorial as F,gcd,pi
from itertools import chain,combinations,permutations,accumulate
from collections import Counter,defaultdict,OrderedDict,deque
from array import array
INT_MAX = sys.maxsize
INT_MIN = -(sys.maxsize)-1
mod = 1000000007
ch = "abcdefghijklmnopqrstuvwxyz"
lcm = lambda a,b : (a*b)//gcd(a,b)
setbit = lambda x : bin(x)[2:].count("1")
Int = lambda type : type(sys.stdin.readline()) if type in [int,float] else type(sys.stdin.readline()).replace("\n","")
Array = lambda type : list(map(type,sys.stdin.readline().split()))
Nums = lambda type : map(type,sys.stdin.readline().split())

def solve():
    T = Int(int)
    for _ in range(T):
        n,k = Nums(int)
        if n%k == 0:
            print("YES")
            print(*[n//k]*k)
        elif n < k:
            print("NO")
        else:
            if (n-k+1)&1 and n-k+1>0:
                print("YES")
                print(*([1]*(k-1)+[n-k+1]))
            elif not (n-2*(k-1))&1 and (n-2*(k-1))>0:
                print("YES")
                print(*([2]*(k-1)+[n-2*(k-1)]))
            else:
                print("NO")



if __name__ == "__main__":
    try:
        sys.stdin = open("input.txt","r")
    except:
        pass
    solve()