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:
import math

for _ in range(int(input())):
    a, b = map(int, input().split())
    if a % b == 0:
        print('YES')
        base = a // b
        for i in range(b):
            print(base, end= ' ')
        print()
    elif a < b:
        print('NO')
    else:
        if a % 2 == 1 and b % 2 == 0:
            print('NO')
        elif a % 2 == 1 and b % 2 == 1:
            ans = []
            print('YES')
            for i in range(b-1):
                ans.append(1)
            ans.append(a-b+1)
            print(' '.join(map(str, ans)))
        else:
            ans = []
            ans2 = []
            for i in range(b-1):
                ans2.append(1)
            rem = a - b+1
            ans2.append(rem)
            if rem % 2 == 1 and rem > 0 and sum(ans2) == a:
                print('YES')
                print(' '.join(map(str, ans2)))
            else:
                for i in range(b-1):
                    ans.append(2)
                rem = a - 2*(b-1)
                ans.append(rem)
                if rem % 2 == 0 and rem > 0 and sum(ans) == a:
                    print('YES')
                    print(' '.join(map(str, ans)))
                else:
                    print('NO')