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 sys

input = sys.stdin.readline


def inp():
    return (int(input()))


def inlt():
    return (list(map(int, input().split())))


def insr():
    s = input()
    return (list(s[:len(s) - 1]))


def invr():
    return list((map(int, input().split())))


def solve(arr):
    res = []
    for a in arr:
        if a[0] % 2 != 0 and a[1] % 2 == 0:
            res.append([])
            continue
        if a[1] > a[0]:
            res.append([])
            continue
        if a[1] % 2 != 0:
            n = a[0]
            if n % 2 != 0:
                r = [1] * (a[1] - 1)
                r.append(n - sum(r))
                res.append(r)
            else:
                r = [2] * (a[1] - 1)
                if sum(r) >= n:
                    res.append([])
                else:
                    r.append(n - sum(r))
                    res.append(r)
        else:
            n = a[0]
            r1 = [1] * (a[1] - 1)
            r2 = [2] * (a[1] - 1)
            if sum(r1) < n:
                r1.append(n - sum(r1))
                res.append(r1)
            elif sum(r2) < n:
                r2.append(n - sum(r2))
                res.append(r2)
            else:
                res.append([])
    return res




if __name__ == '__main__':
    n = inp()
    arr = []
    for i in range(n):
        arr.append(inlt())
    res = solve(arr)
    for r in res:
        if r:
            print("YES")
            print(" ".join(map(str, r)))
        else:
            print("NO")