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 math
t=int(input())
for _ in range(t):
    flag=0
    n,k=map(int,input().split())
    lis1=[]
    lis2=[]
    lis=[]
    if n<k:
        flag=1
    elif n%2!=0:
        if k%2==0:
            flag=1
        elif k==n:
            for _ in range(k):
                lis.append(1)
        else:
            for _ in range(k-1):
                lis.append(1)
            if 1==(n-sum(lis))%2 and n-sum(lis)>0:
                lis.append(n-sum(lis))
            else:
                flag=1
            
    else:
        if k==n:
            for _ in range(k):
                lis1.append(1)
            lis=lis1
        else:
            for _ in range(k-1):
                lis2.append(2)
                lis1.append(1)
            if 0==(n-sum(lis2))%2 and n-sum(lis2)>0:
                lis2.append(n-sum(lis2))
                lis=lis2
            elif (n-sum(lis1))%2==1 and n-sum(lis1)>0:
                lis1.append(n-sum(lis1))
                lis=lis1
            else:
                flag=1
            
        
                
            
        
    if flag==1:
        print('NO')
    else:
        print('YES')
        for i in range(len(lis)):
            print(lis[i],end=' ')
        print()