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:
import copy
iterator = int(input())
while iterator != 0:
    a = (input())
    A = a.split(' ')
    t = int (A[0])
    n = int (A[1])
    t2 = copy.copy(t)
    CounterEven=0
    CounterOdd=0
    EvenArray=[]
    OddArray=[]
    FlageEven = False
    FlageOdd = False
    while (CounterEven< n -1 ):
        t = t - 2
        EvenArray.append(2)
        CounterEven = CounterEven + 1
    
    if (t % 2 == 0) and t > 0 :    
        EvenArray.append(t)
    if (len(EvenArray) == n):
        FlageEven = True
        #print(EvenArray)
         
    if FlageEven == False :
        
        while (CounterOdd< n -1 ):
            t2 = t2 - 1
            OddArray.append(1)
            CounterOdd = CounterOdd + 1
        
        if (t2 % 2 != 0) and t2 > 0:    
            OddArray.append(t2)
        if (len(OddArray) == n):
            FlageOdd = True
            #print(OddArray)
            
    if FlageEven:
        print("YES")
        for I in EvenArray:
            print(I , end =" ")
    elif FlageOdd:
        print("YES")
        for I in OddArray:
            print(I , end =" ")
    else :
        print ("NO")
    iterator = iterator - 1