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:
t = int(input())
while t > 0:
    t-=1
    a = input().split()
    if int(a[0]) < int(a[1]):
        print("NO")
    elif int(a[1])==1:
        print("YES")
        print(int(a[0]))
    else:
        m = int(a[0]) - int(a[1])
        if m % 2 ==0:
            print("YES")
            for i in range(0,int(a[1])):
                if(i == int(a[1])-1):
                    print(1+m)
                else:
                    print(1,end=' ')
        elif m >= int(a[1]) and int(a[1]) % 2 ==1:
            print("YES")
            m -= int(a[1])
            for i in range(0, int(a[1])):
                if (i == int(a[1]) - 1):
                    print(2 + m)
                else:
                    print(2, end=' ')
        else:
            print("NO")