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 PYTHON):

Solution:
FAST_IO = 0
if FAST_IO:
    import io, sys, atexit
    rr = iter(sys.stdin.read().splitlines()).next
    sys.stdout = _OUTPUT_BUFFER = io.BytesIO()
    @atexit.register
    def write():
        sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
else:
    rr = raw_input
rri = lambda: int(rr())
rrm = lambda: map(int, rr().split())

####

from collections import defaultdict as ddic, Counter, deque
from itertools import product, combinations, permutations
import heapq
YES, NO, IMP = "YES", "NO", "IMPOSSIBLE"
MOD = 10**9 + 7

####

def solve(N,  K):
    Np = N & 1
    if Np:
        if K&1 != Np: return
    while 1:
        ans = [1] * (K - 1)
        ans.append(N - (K-1))
        if any(x <= 0 for x in ans): break
        if not ans: break
        if any(x&1 != ans[0]&1 for x in ans): break
        return ans
    while 1:
        ans = [2] * (K - 1)
        ans.append(N - 2 * (K-1))
        if any(x <= 0 for x in ans): break
        if not ans: break
        if any(x&1 != ans[0]&1 for x in ans): break
        return ans
    return
T = rri()
for _ in xrange(T):
    N, K = rrm()
    ans = solve(N, K)
    if ans is None:
        print NO
    else:
        print YES
        print " ".join(map(str, ans))