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 math

def ans(a,b):
    x=a
    y=b
    sum=0
    count=0
    s=''
    s1=''
    if(a%b==0):
        print("YES")
        for i in range(1,b+1,1):
            print(a//b,end=' ')
        print()
    elif(a%2==0):
        for i in range(1,b,1):
            s+='2'
            s+=' '
            sum+=2
        s+=str(abs(a-sum))
        m=sum+abs(a-sum)
        for i in range(1,b,1):
            s1+='1'
            s1+=' '
            count+=1
        s1+=str(abs(a-count))
        n=count+abs(count-a)
        if(m==x and abs(a-sum)>0 and abs(a-sum)%2==0):
            print("YES")
            print(s)
        elif(n==x and abs(count-a)>0 and abs(a-count)%2!=0):
            print("YES")
            print(s1)
        else:
            print("NO")
    elif(a%2!=0):
        for i in range(1,b,1):
            s+='2'
            s+=' '
            sum+=2
        s+=str(abs(a-sum))
        m=sum+abs(a-sum)
        for i in range(1,b,1):
            s1+='1'
            s1+=' '
            count+=1
        s1+=str(abs(a-count))
        n=count+abs(count-a)
        if(m==x and abs(a-sum)>0 and abs(a-sum)%2==0):
            print("YES")
            print(s)
        elif(n==x and abs(count-a)>0 and abs(a-count)%2!=0):
            print("YES")
            print(s1)
        else:
            print("NO")
    else:
        print("NO")
        
        
t=int(input())
f=0
while(t>0):
    sum=0
    a,b=map(int,input().split())
    if(a<b):
        print("NO")
    else:
        ans(a,b)
    t-=1