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 PYTHON):

Solution:
t = input()

def do_odd(n, k):
    if n < k:
        return []
    even = do_even(n-1,k-1)
    if even == []:
        return []
    return [1] + even


def do_even(n, k):
    if n < 2*k:
        return []
    return [2] * (k-1) + [n - (k-1)*2]

def do_weird(n, k):
    if n < k:
        return []
    
    return [1] * (k - 1) + [n - (k-1)]


for _ in xrange(t):
    n, k = map(int, raw_input().split())

    if n % 2 == 1 and k % 2 == 0:
        print "NO"
    elif n % 2 == 1 and k % 2 == 1:
        res = do_weird(n, k)
        if res == []:
            print "NO"
        else:
            print "YES"
            print " ".join(map(str, res))
    else:
        res = do_even(n, k)
        if res == []:
            if k % 2 == 0:
                res = do_weird(n, k)
                if res != []:
                    print "YES"
                    print " ".join(map(str, res))
                else:
                    print "NO"
            else:
                print "NO"
        else:
            print "YES"
            print " ".join(map(str, res))