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 q in range(t):
    n, k = list(map(int, input().split(" ")))
    p = n//k
    if(k <= n):
        if(n % 2 != 0 and k % 2 != 0):
            print("YES")
            if(k == 1):
                print(n)
            else:
                p = n-(k-1)
                print(p, end = " ")
                for k in range(k-1):
                    print(1, end = " ")
                print()
                
        elif(n % 2 == 0 and k % 2 != 0):
            if(p % 2 != 0):
                p -= 1
            if(p != 0):
                print("YES")
                while(n > 0):
                    if(k == 1):
                        print(n)
                        n = 0
                        k -= 1
                    else:
                        print(p, end = " ")
                        n -= p
                        k -= 1
            else:
                print("NO")
        elif(n % 2 == 0 and k % 2 == 0):
            print("YES")
            while(n > 0):
                if(k == 1):
                    print(n)
                    n = 0
                    k -= 1
                else:
                    print(p, end = " ")
                    n -= p
                    k -= 1
        elif(n % 2 != 0 and k % 2 == 0):
            print("NO")
    else:
        print("NO")