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 = input()
t = int(t)
shetchikshetchikov1 = 0
while shetchikshetchikov1 < t :
    n,k1 = input().split()
    n = int(n)
    k1 = int(k1)
    a = []
    k = 1
    r = 0
    if n == k1 :
        print('YES')
        while k <= k1 :
            a.append(1)
            k = k + 1
        print(*a)
    else :
        if n % 2 == 0 :
            while k <= k1 :
                if k != k1 :
                    if n % 2 == 0 and k1 % 2 == 0 :
                        a.append(1)
                        r = r + 1
                    else :
                        a.append(2)
                        r = r + 2
                else :
                    c = n - r
                    a.append(c)
                k = k + 1
        else :
            while k <= k1 :
                if k != k1 :
                     a.append(1)
                     r = r + 1
                else :
                    c = n - r
                    a.append(c)
                k = k + 1
        if (n % 2 == 1 and k1 % 2 == 0) or (n < k1) or (n-1) == k1 or a[-1] <= 0:
            if k1 != 1 :
                print('NO')
            else :
                print('YES')
                print(n)
        else :
            print('YES')
            print(*a)
    shetchikshetchikov1 = shetchikshetchikov1 + 1