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:
from sys import stdin, stdout
"""
    n = stdin.readline()
    arr = [int(x) for x in stdin.readline().split()]
    stdout.write(str(summation))
"""
for test in range(int(stdin.readline())) :
    arr = [int(x) for x in stdin.readline().split()]
    n = arr[0]
    k = arr[1]
    ans = [n//k]*k
    rem = n%k

    if rem==0 :
        print("YES")
        print(*ans, sep=" ")
    
    elif k>n  or k==2 :
        print("NO")

    else :
        temp = n-k+1
        answ = [1]*(k-1)
        
        if temp%2 == 1 :
            print("YES")
            answ.append(temp)
            print(*answ, sep=" ")

        elif (k-1)%2==0 :
            if n >= 2*k :
                print("YES")
                answ = [2]*(k-1)
                answ.append(temp+1-k)
                print(*answ, sep=" ")
            else :
                print("NO")
        
        else :
            print("NO")