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
# from math import sqrt, floor, factorial, gcd
from collections import Counter
inp = sys.stdin.readline
read = lambda: list(map(int, inp().strip().split()))

def a():
    ans = ""
    for _ in range(int(inp())):
        n = int(inp()); tem = ""; x = 0; c = 0
        while n:
            if n%10:
                c += 1
                tem += str(n%10 * 10**x)+" "
            x +=1; n //= 10
        ans += str(c)+"\n"+tem +"\n"
    print(ans)

def b():
    ans = ""
    for _ in range(int(inp())):
        n, k = read()
        if n == k:
            ans += "YES\n"
            ans += "1 "*k + "\n"
        elif k > n:
            ans += "NO\n"
        elif n%2 == 0:
            if k <= n//2:
                ans += "YES\n"
                # v = 1 if n%2 else 2
                for i in range(k-1):
                    ans += "2 "
                    n -= 2
                ans += str(n)+"\n"
            elif k % 2 == 0:
                ans += "YES\n"
                for i in range(k-1):
                    ans += "1 "
                    n -= 1
                ans += str(n)+"\n"
            else:
                ans += "NO\n"
        else:
            if k%2 == 0:
                ans += "NO\n"
            else:
                ans += "YES\n"
                for i in range(k-1):
                    ans += "1 "
                    n -= 1
                ans += str(n)+"\n"
    print(ans)

def c():
    ans = ""
    for _ in range(int(inp())):
        k, n = read()
        n += (n + n//k)//k
        if n%k == 0:
            n += 1
        ans += str(n)+"\n"
    print(ans)

if __name__ == "__main__":
	# a()
    b()
    # c()