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:


def is_odd(n):
    if(n>0 and n%2 ==1):
        return True
    return False
def is_even(n):
    if(n>0 and n%2 ==0):
        return True
    return False
def odd_parity(n,k):
    if (k>n):
        return False
    if (n-k)%2 == 0:
        return True
    else:
        return False
def even_parity(n,k):
    if(2*k>n):
        return False
    if (n - 2*k)%2 == 0:
        return True
    else:
        return False


def solve(n,k):
    #if(is_odd(n) and is_even(k)):
     #   print('NO')
    if(odd_parity(n,k)):
        print('YES')
        stri = ""
        for i in range(k-1):
            stri += '1 '
        num = n+1-k
        stri = stri + str(num)
        print(stri)
    elif(even_parity(n,k)):
        print('YES')
        stri = ""
        for i in range(k-1):
            stri += '2 '
        num = n + 2 - 2*k
        stri = stri + str(num)
        print(stri)
    else:
        print('NO')


for i in range(int(input())):
    inp = input().split()
    solve(int(inp[0]), int(inp[1]))