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:
# -*- coding: utf-8 -*-
"""
Created on Sat May  9 20:57:02 2020

@author: Mongia Bros
"""

def funx(n,k):
    
    if n<k:
        print("NO")
        return 0
    else:
        f=[]
        if n%2 ==0 :
            if n<(2*k):
                if(k%2==1):
                    print("NO")
                    return 0
                else:
                    for i in range(k-1):
                        f.append(1)
                    f.append(n-k+1)
                    print("YES")
                    print(*f)
                    return 0
                    
            
            else:
                for i in range(k-1):
                    f.append(2)
                f.append(n-(2*(k-1)))
                print("YES")
                print(*f)
                return 0
        else:
            if(k%2==0):
                print("NO")
                return 0
            else:
                for i in range(k-1):
                    f.append(1)
                f.append(n-k+1)
                print("YES")
                print(*f)
                return 0
            





for _ in range(int(input())):
    n,k = map(int,input().split())
    
    if n==k:
        f=[]
        for i in range(k):
            f.append(1)
        print("YES")
        print(*f)
    else:
        funx(n,k)