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:
integer = int
string = str
length = len

def fun(n,k):
    if n%2!=0 and k%2==0:
        print('NO')
    else:
        if n/k==integer(n/k):
            print('YES')
            ans=[integer(n/k)]*k
            print(*ans)
        else:
            temp1=integer(n/k)
            x=n%k
            if x%2==0 and temp1!=0:
                print('YES')
                ans=[temp1]*k
                ans[-1]+=x
                print(*ans)
            else:
                if n%2==0 and k%2!=0:
                    temp=temp1-1
                    if temp!=0:
                        ans=[temp]*k
                        ans[-1]+=(n-temp*k)
                        print('YES')
                        print(*ans)
                    else:
                        print('NO')
                elif n%2!=0 and k%2!=0:
                    temp=temp1-1
                    if (n-(temp*k))%2==0 and temp!=0:
                        ans=[temp]*k
                        ans[-1]+=(n-temp*k)
                        print('YES')
                        print(*ans)
                    else:
                        temp=temp1+1
                        if (n-(temp*k))%2==0 and temp!=0:

                            ans=[temp]*k
                            ans[-1]+=(n-temp*k)
                            print('YES')
                            print(*ans)
                        else:
                            print('NO')
                else:
                    temp=temp1-1
                    if (n-(temp*k))%2==0 and temp!=0:
                        ans=[temp]*k
                        ans[-1]+=(n-temp*k)
                        print('YES')
                        print(*ans)
                    elif (n-(temp1*k))%2==0 and temp1!=0:
                        ans=[temp1]*k
                        ans[-1]+=(n-temp1*k)
                        print('YES')
                        print(*ans)
                    else:
                        temp=temp1+1
                        if (n-(temp*k))%2==0 and temp!=0:

                            ans=[temp]*k
                            ans[-1]+=(n-temp*k)
                            print('YES')
                            print(*ans)
                        else:
                            print('NO')








def main():
    for _ in range(int(input())):
        n,k=list(map(integer,input().split()))
        if k>n:
            print('NO')
        else:
            fun(n,k)


main()