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
def facts(n):
    ans = []
    for i in range(2, int(math.sqrt(n)+1)):
        if(n%i==0):
            ans.append(i)
            ans.append(n//i)
    ans = sorted(ans)
    return ans

for _ in range(int(input())):
    n, k =map(int, input().split())
    if(n==k):
        print('YES')
        print('1 '*k)
    elif(n%2==0):
        if((n-(2*(k-1)))%2==0 and (n-(2*(k-1)))>0):
            ans=['2' for i in range(k-1)]
            ans.append(str(n-(2*(k-1))))
            print('YES')
            print(' '.join(ans))
        else:
            if((n-k+1)%2==1 and (n-k+1)>0):
                ans = ['1' for i in range(k-1)]
                ans.append(str(n-k+1))
                print('YES')
                print(' '.join(ans))
            else:
                print('NO')
    else:
        if((n-k+1)%2==1 and (n-k+1)>0):
            ans = ['1' for i in range(k-1)]
            ans.append(str(n-k+1))
            print('YES')
            print(' '.join(ans))
        else:
            print('NO')