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:

for t in range(int(input())):
    n,k=list(map(int,input().split()))
    if k>n:
        print("NO")
        continue
    if k==n:
        print("YES")
        print("1 "*n)
        continue
    if n%k==0:
        print("YES")
        print((str(n//k)+" ")*k)
        continue
    aa=n//k
    a=aa*(k-1)
    b=n-a
    if aa%2==0 and b%2==0 and b>0 and aa>0:
        print("YES")
        print((str(aa)+" ")*(k-1)+str(b))
        continue
    if aa%2==1 and b%2==1 and b>0 and aa>0:
        print("YES")
        print((str(aa)+" ")*(k-1)+str(b))
        continue
    else:
        aa=(n//k)+1
        a=aa*(k-1)
        b=n-a
        if aa%2==0 and b%2==0 and b>0 and aa>0:
            print("YES")
            print((str(aa)+" ")*(k-1),b)
            continue
        if aa%2==1 and b%2==1 and b>0 and aa>0:
            print("YES")
            print((str(aa)+" ")*(k-1),b)
            continue
        aa=(n//k)-1
        a=aa*(k-1)
        b=n-a
        if aa%2==0 and b%2==0 and b>0 and aa>0:
            print("YES")
            print((str(aa)+" ")*(k-1),b)
            continue
        if aa%2==1 and b%2==1 and b>0 and aa>0:
            print("YES")
            print((str(aa)+" ")*(k-1),b)
            continue
    print("NO")