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:
from math import trunc
from sys import exit

t = int(input())

for _ in range(t):
    n, k = [int(x) for x in input().split()]

    if k > n:
        print('NO')
        continue

    if n % k == 0:
        print('YES')
        for i in range(k):
            print(trunc(n / k), end=' ')
        print(end='\n')
    else:
        mod = n % k
        ai = trunc(n / k)
        ans = [ai] * k
        ans[0] += mod
        if ((ai + mod) % 2 == 0 and ai % 2 == 0) or ((ai + mod) % 2 != 0 and ai % 2 != 0):
            print('YES')
            for i in ans:
                print(i, end=' ')
            print(end='\n')
        else:
            if ai - 1 <= 0:
                print('NO')
                continue
            else:
                for i in range(1, k):
                    if i % 2 != 0:
                        ans[i] -= 1
                    else:
                        ans[i] += 1

                if sum(ans) == n:
                    print('YES')
                    for i in ans:
                        print(i, end=' ')
                    print(end='\n')
                else:
                    print('NO')