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:
t = int(input())
while t:
    n, k = map(int, input().split())
    ans = []
    if n % k == 0:
        ap = n // k
        for i in range(k):
            ans.append(ap)
        print("YES")
        print(*ans)
    else:
        temp = n % k
        temp1 = n//k
        ans = []
        for i in range(k):
            ans.append(temp1)
        mainn = n
        n = len(ans)
        if k > mainn:
            print("NO")
        elif temp % 2 == 0:
            ans[-1] += temp
            print("YES")
            print(*ans)

        else:
            for i in range(n - 1, n - 1 - temp, -1):
                ans[i] += 1
            if (n - temp) % 2 != 0:
                print("NO")
            else:
                f = 0
                n = len(ans)
                for i in range(n-temp):
                    if i % 2 == 0:
                        ans[i] -= 1
                        if ans[i] == 0:
                            print("NO")
                            f = 1
                            break
                    else:
                        ans[i] += 1
                if f != 1:
                    print("YES")
                    print(*ans)
    t -= 1