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:
import math
t = int(input())
while t:
    a,b = list(map(int,input().split()))
    s = ''
    if a>=b:
        if a%2==0:
            if b<=a//2 and b%2==1:
                print("YES")
                s = s + '2 '*(b-1)
                s = s + str(a-2*(b-1))
                print(s)
            elif b%2==0:
                print("YES")
                s = s + '1 '*(b-1)
                s = s + str(a-(b-1))
                print(s)
            else:
                print("NO")
        elif a%2==1 and b%2==1:
            print("YES")
            s = s + '1 ' * (b - 1)
            s = s + str(a - (b - 1))
            print(s)
        else:
            print("NO")
    else:
        print("NO")




    t = t - 1