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 h in range (t):
    k,n=[int(x) for x in input().split()]
    m=k-n
    s=[]
    if (k%2!=0 and n%2==0) or (abs(m)==1 and (k!=2 and m!=1)) or (m<0):
        print("NO")
    else:
        if (k%2==0 and n%2!=0):
            mm=k/2
            if n>mm:
                print("NO")
            else:
                for j in range (n-1):
                    k=k-2
                    s.append(2)
                s.append (k)
                print("YES")
                for num in s:
                    print(num,end=" ")
        elif (k%2!=0 and n%2!=0):
            for j in range (n-1):
                k=k-1
                s.append(1)
            s.append (k)
            print("YES")
            for num in s:
                print(num,end=" ")
 
        else:
            if (k%2==0 and n%2 == 0) and (n<=(k/2)):
                for j in range (n-1):
                    k=k-2
                    s.append (2)
                s.append (k)
                print("YES")
                for num in s:
                    print(num,end=" ")
 
            else:
                if (k%2==0 and n%2 == 0) and (n>(k/2)):
                    for j in range (n-1):
                        k=k-1
                        s.append (1)
                    s.append (k)
                    print("YES")
                    for num in s:
                        print("\r")
                        print(num,end=" ")