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:
import sys
t = input()

while(t  >0):
    n_k = raw_input().split()
    n = int(n_k[0])
    k = int(n_k[1])
    x1 = n - (k -1)
    x2 = n - 2*(k -1)
    flag = 0 
    if( x1 > 0 and x1 % 2 != 0  ):
        print("YES")
        flag =1
        for i in range(1, k ):
            sys.stdout.write("1")
            sys.stdout.write(" ")
        sys.stdout.write(str(x1))
    if(  x2 > 0 and x2 % 2  == 0  and flag  != 1 ):
        flag =1
        print("YES")
        for i in range(1, k ):
            sys.stdout.write("2")
            sys.stdout.write(" ")
        sys.stdout.write(str(x2))
    if( flag == 0):
        sys.stdout.write("NO")
    sys.stdout.write("\n")
    t -= 1