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:


import sys
import math
from collections import Counter,defaultdict
try: 
    sys.stdin = open('input.txt', 'r') 
    sys.stdout = open('output.txt', 'w')

except: 
    pass
    


def takeInput():
    return [int(x) for x in input().strip().split()]
 
        
t=int(input())
while t!=0:
    t-=1
    n,k=takeInput()
    if(n%2!=0):
        if(k%2==0):
            print("NO")
        else:
            ans=[]
            start=1
            for i in range(k-1):
                ans.append(start)
            rem=n-sum(ans)
            if(rem>0):
                ans.append(n-sum(ans))
                print("YES")
                print(*ans)
            else:
                print("NO")
    else:
        ans=[]
        start=2
        for i in range(k-1):
            ans.append(start)
        rem=n-sum(ans)
        if(rem>0):
            ans.append(n-sum(ans))
            print("YES")
            print(*ans)
        else:
            start=1
            ans=[]
            for i in range(k-1):
                ans.append(start)
            rem=n-sum(ans)
            if(rem>0 and rem%2!=0):
                ans.append(n-sum(ans))
                print("YES")
                print(*ans)
            else:
                print("NO")