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:


t = int(input())

for _ in range(t):
    
    n,k = map(int,input().split())
    
    if(n % k == 0):
        print('YES')
        temp = n // k
        for x in range(k):
            print(temp,end = ' ')
        print()
        continue
    if(n == k):
        for x in range(k):
            print(1,end=' ')
        print()
        continue
    if(n % 2 == 1 and k % 2 == 0):
        print("NO")
        continue
    
    if(n - k < 2):
        print("NO")
        continue
        
    if(k % 2 == 0 and (n % k) % 2 == 1 ):
        print("NO")
        continue
    
    if(n // k == 1 and k % 2 == 1 and (n % k) % 2 == 1):
        print("NO")
        continue
    
    temp = n // k
    array = [temp] * k
    rem = n % k
    if(rem % 2 == 0):
        for i in range(rem):            
            if(i % 2 == 0):
                array[i] += 2
    else:
        for i in range(k):
            if(i < rem):
                array[i] += 1
            else:
                if(i % 2 == 0):
                    array[i] += 1
                else:
                    array[i] -= 1
    
    print('YES')
    #print(array)
    for x in array:
        print(x,end =' ')
    
    print()