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:
t=int(input())
for j in range(t):
    g=list(map(int,input().split()))
    n=g[0]
    k=g[1]
    if(n%2==1 and k%2==0):
        print("NO")
    elif(n<k):
        print("NO")
    elif(n==k):
        h=[1]*k
        print("YES")
        for i in range(len(h)):
            print(h[i],end=" ")
    else:
        if(n%2==0 and k%2==1):
            if(n<2*k):
                print("NO")
            else:
                c=0
                d=0
                h=[]
                while(d!=k-1):
                    c+=2
                    h.append(2)
                    d+=1
                h.append(n-c)
                print("YES")
                for i in range(len(h)):
                    print(h[i],end=" ")
        elif(n%2==0 and k%2==0):
            c=0
            d=0
            h=[]
            while(d!=k-1):
                c+=1
                h.append(1)
                d+=1
            h.append(n-c)
            print("YES")
            for i in range(len(h)):
                print(h[i],end=" ")
        else:
            if(n<k):
                print("NO")
            else:
                c=0
                d=0
                h=[]
                while(d!=k-1):
                    c+=1
                    h.append(1)
                    d+=1
                h.append(n-c)
                print("YES")
                for i in range(len(h)):
                    print(h[i],end=" ")