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 inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return(map(int,input().split()))

entries = inp()

for i in range(entries):
    ins = inlt()

    n = ins[0]
    k = ins[1]
    if(n < k):
        print("NO")
    elif(n%2 == 0):
        if(n == k):
            print("YES")
            res = ''
            for z in range(k):
                res += str(1) + ' '
            print(res)
        elif(n < 2*k):
            if(k%2 == 1):
                print("NO")
            else:
                print("YES")
                res = ''
                for z in range(k-1):
                    res += str(1) + ' '
                res += str(n - (k-1))
                print(res)

        else:
            print("YES")
            res = ''
            tmp = n
            for z in range(k-1):
                res += str(2) + ' '
            res += str(n-2*(k-1))
            print(res)

    elif(n%2 == 1):
        if(k % 2 == 0):
            print("NO")
        else:
            print("YES")
            res = ''
            for z in range(k-1):
                res += str(1) + ' '
            res += str(n - k + 1)
            print(res)