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:
# Заданы два целых положительных числа n (1≤n≤109) и k (1≤k≤100).
# Представьте число n в виде суммы k положительных целых чисел одинаковой четности
# (с одинаковыми остатками от деления на 2).

# Входные данные
# В первой строке записано целое число t (1≤t≤1000) — количество наборов входных данных в тесте. Далее записаны t наборов входных данных по одному в строке.
counter = int(input())

for _ in range(counter):
    #n, k = int(input()),  int(input())
    n, k = [int(x) for x in input().split()]
    
    # пробовать на 1
    r = n - 1*(k-1)
    if r > 0 and r % 2 != 0:
        l = [1]*(k-1) + [r]
        l = [str(x) for x in l]
        print('YES')
        print(' '.join(l))
        continue
        
    r = n - 2*(k-1)
    if r > 0 and r % 2 == 0:
        l = [2]*(k-1) + [r]
        l = [str(x) for x in l]
        print('YES')
        print(' '.join(l))
    else:
        print('NO')