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:
#!/usr/bin/python3

import getopt
import sys
import math

if __name__ == "__main__":
    onlyCase = -1
    verbose = False
    
    try:
         opts, args = getopt.getopt(sys.argv[1:], "vc:",
                                   ["case="])
    except getopt.GetoptError as err:
        print (str(err)) 
        sys.exit(2)

    for o, a in opts:
        if o in ("-c", "--case"):
            onlyCase = int(a)
        elif o  == "-v":
            verbose = True
        else: sys.exit()

    
    ncases = int(input())
    for c in range(1, ncases + 1):
        N, k = [int(x) for x in input().split()]
        
        if onlyCase != -1 and onlyCase != c:
            continue

        s = []
        possible = False
        if (N + k) % 2  == 0:
            # odd sums
            while k > 1:
                k -= 1
                N -= 1
                s.append(1)
            s.append(N)
            if N > 0:
                possible = True
        else:
            if N % 2 == 0:
                # even sums
                while k > 1:
                    k -= 1
                    N -= 2
                    s.append(2)
                s.append(N)
                if N > 0:
                    possible = True

        if not possible:
            print("NO")
        else:
            print("YES")
            print(' '.join(map(str,s)))