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:
no = int(input())
inList = []
mainList = []
yesNoList = []
for i in range(0,no):
    temp = []
    a, b = input().split()
    a = int(a)
    b = int(b)
    temp.append(a)
    temp.append(b)
    inList.append(temp)
for i in inList:
    if(i[0]>=i[1]):
        nEven = True if i[0]%2==0 else False
        kEven = True if i[1]%2==0 else False
        if kEven == True and nEven == False:
            mainList.append([])
            yesNoList.append("NO")
        elif ((kEven == True and nEven == True) or (kEven == False and nEven == False)):
            temp = [1] * i[1]
            if 1*i[1] <= i[0]:
                temp[len(temp)-1] = temp[len(temp)-1]+(i[0]-i[1])
                if temp[len(temp)-1]%2 == 1:
                    mainList.append(temp)
                    yesNoList.append("YES")
                else:
                    mainList.append([])
                    yesNoList.append("NO")
            else:
                    mainList.append([])
                    yesNoList.append("NO")
        elif ((kEven == False and nEven == True) or (kEven == True and nEven == False)):
            temp = [2] * i[1]
            if 2*i[1] <= i[0]:
                temp[len(temp)-1] = temp[len(temp)-1]+(i[0]-(2*i[1]))
                if temp[len(temp)-1]%2 == 0:
                    mainList.append(temp)
                    yesNoList.append("YES")
                else:
                    mainList.append([])
                    yesNoList.append("NO")
            else:
                    mainList.append([])
                    yesNoList.append("NO")
    else:
        mainList.append([])
        yesNoList.append("NO")
            
for i in range(0,no):
    print(yesNoList[i])
    c=0
    for j in mainList[i]:
        c = c+1
        if c != len(mainList[i]):
            print(j,end=" ")
        else:
            print(j)