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:
# Importing Modules
from collections import *
from itertools import *
from functools import *
import sys
import os
import time
# ~ import numpy as np


# Debugging and Timer Flags
timer = False
debug = False

# ---------- Helper Functions -----------
def timeit(method):
    def wrapper(*args, **kwargs):
        mname = method.__name__
        if debug:
            print("{}(args:{}, kwargs:{})".format(mname, args,kwargs))
        if timer:
            ts = time.time()
        result = method(*args, **kwargs)
        if timer:
            te = time.time()
            print('%r  %2.2f ms'% (mname, (te-ts) * 1000))
        return result
    return wrapper

def read_ints():
    return list(map(int,input().split()))

def read_floats():
    return list(map(float,input().split()))

def read_strs():
    return input().split()
# ----------------------------------------




@timeit
def main():
    t = int(input())
    for _ in range(t):
        n,k = read_ints()
        if n<k:
            print("NO")
            continue
        if k==n:
            print("YES")
            ans = [1]*n
            print(*ans)
            continue
        if n>k:
            if n%2 == 0 and k%2 == 0:
                ans = [1]*(k-1)
                ans.append(n-k+1)
                print("YES")
                print(*ans)
            elif n%2 == 0 and k%2 !=0:
                if n<2*k:
                    print("NO")
                    continue
                else:
                    ans = [2]*(k-1)
                    ans.append(n-(2*k)+2)
                    print("YES")
                    print(*ans)
                    continue
            elif n%2!=0 and k%2==0:
                print("NO")
                continue
            else:
                ans = [1]*(k-1)
                ans.append(n-k+1)
                print("YES")
                print(*ans)




if __name__=="__main__":
    main()