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:
t=int(input())
for test in range(t):
    n,k=[int(x) for x in input().split()]
    num=[]
    if n<k:
        print('NO')
        continue
    if k==1:
        print('YES')
        print(n)
        continue
    if n%2 ==0:
        if k%2 == 0:
            kt=k-1
            temp=n//k
            num.append(temp)
            digit=temp
            while  kt !=1 :
                num.append(temp)
                digit+=temp
                kt-=1
            num.append(n-digit)
        else:
            kt = k - 1
            temp = n // k
            if temp%2!=0:
                if temp == 1:
                    temp=2
                else:
                    temp-=1

            num.append(temp)
            digit = temp
            while kt != 1:
                num.append(temp)
                digit += temp
                kt -= 1
            if n-digit <= 0:
                print('NO')
                continue
            num.append(n - digit)
    else:
        if k%2 == 0:
            print('NO')
            continue

        else:
            kt = k - 1
            temp = n // k
            if temp%2 == 0:
                temp-=1

            num.append(temp)
            digit = temp
            while kt != 1:
                num.append(temp)
                digit += temp
                kt -= 1
            if n-digit < 0:
                print('NO')
                continue
            num.append(n - digit)
    print('YES')
    for i in range(len(num)):
        if i ==len(num)-1:
            print(num[i])
        else:
            print(num[i],end=' ')