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
t = int(input())

for z in range(t):
    n,k = map(int, input().rstrip().split())
    m = n%k
    res = [n//k]*(k)
    temp = [n//k]*(k)
    bool = True
    flag = True

    if(n%k==0):
        print("YES")
        print(" ".join(map(str,res)))
    else:
        i=0
        while(m>0):
            res[i] = res[i] + 1
            temp[i] = temp[i] + 1
            i+=1
            m-=1

        temp.reverse()

        i=0
        if(res[0]%2==0):
            while(i+1<k and res[i]%2==0 and res[i+1]%2==0):
                res[i] -= 1
                if(res[i]<=0):
                    bool = False
                    break
                res[i+1] += 1
                i+=2
            for i in range(k):
                if(res[i]%2==0):
                    bool = False
                    break
        else:
            while(i+1<k and res[i]%2!=0 and res[i+1]%2!=0):
                res[i] -= 1
                if(res[i]<=0):
                    bool = False
                    break
                res[i+1] += 1
                i+=2
            for i in range(k):
                if(res[i]%2!=0):
                    bool = False
                    break
        i=0
        if(temp[0]%2==0):
            while(i+1<k and temp[i]%2==0 and temp[i+1]%2==0):
                temp[i] -= 1
                if(temp[i]<=0):
                    flag = False
                    break
                temp[i+1] += 1
                i+=2
            for i in range(k):
                if(temp[i]%2==0):
                    flag = False
                    break
        else:
            while(i+1<k and temp[i]%2!=0 and temp[i+1]%2!=0):
                temp[i] -= 1
                if(temp[i]<=0):
                    flag = False
                    break
                temp[i+1] += 1
                i+=2
            for i in range(k):
                if(temp[i]%2!=0):
                    flag = False
                    break

        if(bool==False and flag ==False):
            print("NO")
        elif(flag ==False):
            print("YES")
            print(" ".join(map(str,res)))
        else:
            print("YES")
            print(" ".join(map(str,temp)))