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:
from sys import stdin
t = int(stdin.readline())
for _ in xrange(t):
    n,k = map(int,stdin.readline().split())
    odd = 0
    if n%2 ==1 and k%2==1:
        odd = 1
    elif k%2==0:
        odd = 1
    b = []
    for i in xrange(1,k+1):
        b.append(2 -odd)
    #print b
    if sum(b) >n:
        print "NO"
    else:
        b[-1] += n - sum(b)
        valid = 1
        for i in b:
            if i%2 != b[0]%2:
                valid = 0;
                break
        if valid:
            print "YES"
            for i in b:
                print i,
            print ""
        else:
            print "NO"