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:
# cook your dish here
t = int(input())
while(t):
    n,k = map(int, input().split())
    if(n<k):
        print("NO")
    else:
        a = n//k
        if(a*k == n):
            print("YES")
            s=(str(a)+" ")*k
            print(s)
        else:
            c=0
            l = [a]*k
            n = n-(a*k)
            if(((n+a)%2==0 and a%2==0)or((n+a)%2!=0 and a%2!=0)):
                print("YES")
                l[0]+=n
                s=""
                for i in l:
                    s+=str(i)+" "
                print(s)
            else:
                i=0
                while(n!=0):
                    l[i%k]+=1
                    i+=1
                    n-=1
                while(i<len(l)):
                    if(i==len(l)-1):
                        c=1
                        break
                    else:
                        l[i+1]+=1
                        l[i]-=1
                        i+=2
                # print(l)
                if(c==1):
                    print("NO")
                else:
                    c=0
                    s=""
                    for i in l:
                        if(i!=0):
                            s+=str(i)+" "
                        else:
                            c=1
                            break
                    if(c==1):
                        print("NO")
                    else:
                        print("YES")
                        print(s)
    t-=1