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:
import sys
from os import path
if(path.exists('C:/Users/prana/Desktop/sublime/input.txt')):
    sys.stdin = open("C:/Users/prana/Desktop/sublime/input.txt","r")
    sys.stdout = open("C:/Users/prana/Desktop/sublime/output.txt","w")

# ----------------------------------------------------------------------

def solve():
    n,k=input().split()
    n=int(n)
    k=int(k)
    if n%2 !=0 and k%2 ==0 or n<k:
        print("NO")
    else:
        if n%2 !=0 :
            if n>=k:
                ans=[1]*(k-1)
                ans.append(n-k+1)
                print("YES")
                for i in ans:

                    print(i,end=" ")
                print(end="\n")
            else:
                print("NO")

        

        else:
            if n%2 == 0 and k%2 !=0 and  n//2<k:
                print(n,n//2,k,"hy",file = sys.stderr)
                print("NO")
            else:


                print("YES")
                x=n//k
                
                if  x%2 !=0 and x !=1:
                    ans=[x-1]*(k-1)
                    ans.append(n-(k-1)*(x-1))
                else:
                    ans=[x]*(k-1)
                    ans.append(n-x*(k-1))
                for i in ans:
                    print(i,end=" ")
                print(end="\n")

      




    



T = 1
T = int(input())
for _ in range(1,T+1):
    print("Case #", _ , file = sys.stderr)
    solve()