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:

def gcd (a, b) :
    return b if a % b == 0 else gcd (b, a % b)

def Odd (x, y) :
    res = []
    flg1 = True
    res += ['1'] * (y - 1)
    x -= (y - 1)
    if x <= 0 or (not x & 1) :
        flg1 = False
    else :
        res += [(str(x))]
    return flg1, res

def Even (x, y) :
    res = []
    flg1 = True
    res += ['2'] * (y - 1)
    x -= (y - 1) * 2
    if x <= 0 or x & 1 :
        flg1 = False
    else :
        res += [(str(x))]
    return flg1, res

for case in range (int (input ())) :
    n, k = list (map (int, input ().split ()))
    ans = []
    flg = True
    if k > n :
        print("NO")
        continue
    if  (n & 1) or ((not n & 1) and (not k & 1)) :
        flg, ans = Odd (n, k)
    elif ((not n & 1) and (k & 1)):
        flg, ans = Even (n, k)

    if flg :
        print ("YES")
        print (' '.join(list (ans)))
    else :
        print("NO")