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 _ in range(int(input())):
  n,k=map(int,input().split())
  if n%2==1 and k%2==0:
    print("NO")
    #nが奇数、kが偶数の時は奇数を偶数個(k%2==0の時)のsame parityにするのは無理
    #偶数が偶数個=偶数、奇数が偶数個=偶数であるため
  else:
    if k%2==0:
      #(1)
      if n<k:
        print("NO")
         #n<kの時は当然無理
      else:
        ans=[1 for i in range(k-1)]
        ans.append(n-(k-1))
        print("YES")
        print(*ans)
        #nが偶数,kが偶数の時は(k-1)個を1にして最後1個をn-(k-1)にすれば良い
        #奇数が偶数個あれば偶数になるのでnに出来る
    else:
        if n%2==1:
          if n<k:
            print("NO")
          else:
            ans=[1 for i in range(k-1)]
            ans.append(n-(k-1))
            print("YES")
            print(*ans)
            #nが奇数、kが奇数の時は(k-1)個を1にして最後1個をn-(k-1)にすれば良い
            #奇数が奇数個あれば奇数になるのでnに出来る
        else:
            #nが偶数、kが奇数の時は偶数を奇数個作って偶数としたい為、k*2>nなら無理
            if k*2>n:
              print("NO")
            #(k-1)個を2にして最後1個をn-2*(k-1)にすれば良い
            else:
              ans=[2 for i in range(k-1)]
              ans.append(n-2*(k-1))
              print("YES")
              print(*ans)