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:
"""def power(x, y): 
    res = 1
    x=x
    while (y > 0): 
        if ((y & 1) == 1) : 
            res = (res * x) 
        y = y >> 1
        x = (x * x)
    return res""" 
"""def fact(n):
    if(n==0):
        return 1
    if(n==1):
        return 1
    return fact(n-1)+fact(n-2)"""

#import collections
import math
import bisect 
  
t=int(input())
for _ in range(t):
    #n=int(input())
    n,k=map(int,input().split())
    #arr=list(map(int,input().split()))
    #m,k=map(int,input().split())
    l=[]
    l1=[]
    summ=0
    if(n%2==0 and k%2!=0):
        if(n-2*(k-1)>0 and (n-2*(k-1))%2==0):
            
            for i in range(k-1):
                l.append(2)
                summ+=2
            l.append(n-summ)
            print("YES")
            print(*l)
        else:
            print("NO")
    elif(n%2!=0 and k%2!=0):
        if(n-(k-1)>0 and (n-(k-1))%2!=0):
            for i in range(k-1):
                l.append(1)
                summ+=1
            l.append(n-summ)
            print("YES")
            print(*l)
        else:
            print("NO")
    elif(n%2==0 and k%2==0):
        if(n-(k-1)>0 and (n-(k-1))%2!=0):
            for i in range(k-1):
                l.append(1)
                summ+=1
            l.append(n-summ)
            print("YES")
            print(*l)
        elif(n-2*(k-1)>0 and (n-2*(k-1))%2==0):
            for i in range(k-1):
                l.append(2)
                summ+=2
            l.append(n-summ)
            print("YES")
            print(*l)
        else:
            print("NO")
    else:
        print("NO")