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:
test = int(input())
for tes in range(test):
    n, k = list(map(int, input().split()))
    if(n%2==1 and k%2==0):
        print("NO")
    else:
        rem = n//k
        if (rem==0):
            print("NO")
            continue
        su=0
        if(k%2==1):
            if(n%2==1):
                su+=k
                diff = n-su
                if(diff%2==1 or diff<0):
                    print("NO")
                else:
                    print("YES")
                    L = [1 for i in range(k-1)]
                    L.append(diff+1)
                    print(*L)
            else:
                su+=2*k
                diff = n-su
                if(diff%2==1 or diff<0):
                    print("NO")
                else:
                    print("YES")
                    L = [2 for i in range(k-1)]
                    L.append(diff+2)
                    print(*L)
        else:
            su+=k
            diff = n-su
            if(diff%2==1 or diff<0):
                print("NO")
            else:
                print("YES")
                L = [1 for i in range(k-1)]
                L.append(diff+1)
                print(*L)