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:
#link to the problem https://codeforces.com/problemset/problem/1352/B

#solve problem with only even numbers
def solve_even(values):
    n = values[0]
    k = values[1]
    sum_value = 0
    list_v = [2] * (k - 1)
    rest = n - 2 * (k - 1)
    if rest % 2 == 0 and rest > 0:
        list_v.append(rest)
        string_ints = [str(int) for int in list_v]
        return "YES", " ".join(string_ints)
    else:
        return "NO", None

#solve problem with only odd numbers
def solve_odd(values):
    n = values[0]
    k = values[1]
    sum_value = 0
    list_v = [1]* (k - 1)
    rest = n - (k - 1)
    if rest % 2 != 0 and rest > 0:
        list_v.append(rest)
        string_ints = [str(int) for int in list_v]
        return "YES", " ".join(string_ints)
    else:
        return "NO", None

#read the input
times = int(input())
#read input n times
for i in range(times):
    values = input().split(" ")
    values = [int(i) for i in values]
    res, arra = solve_even(values)
    if res == "YES":
        print(res)
        print(arra)
    else:
        res, arra = solve_odd(values)
        print(res)
        if res == "YES":
            print(arra)