Problem: You are given two integers n and k. You are asked to choose maximum number of distinct integers from 1 to n so that there is no subset of chosen numbers with sum equal to k.

A subset of a set is a set that can be obtained from initial one by removing some (possibly all or none) elements of it.

Input

The first line contains the number of test cases T (1 ≤ T ≤ 100).

Each of the next T lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the description of test cases.

Output

For each test case output two lines. In the first line output a single integer m — the number of chosen integers.

In the second line output m distinct integers from 1 to n — the chosen numbers.

If there are multiple answers, print any. You can print the numbers in any order.

Example

Input


3
3 2
5 3
1 1


Output


2
3 1 
3
4 5 2 
0

Solution (in PYTHON3):

Solution:
import sys
import math
input = sys.stdin.readline
t = int(input())
for _ in range(t):
    n,m = map(int,input().split())
    l=[]
    if n>=m:
        if m%2==0:
            c = m//2

            for i in range(c,n+1):
                if i!=m:
                    l.append(i)
        else:
            c = m//2+1
            for i in range(c,n+1):
                if i!=m:
                    l.append(i)
    else:
        k=0
        for i in range(n,0,-1):
            k+=i
            if m-k in range(1,i):
                g = m-k
                j = (m-k+i)
                break
        if g%2==0:
            u = g//2
        else:
             u = g//2+1
        for i in range(u,g):
            l.append(i)
        if (g+j)%2==0:
            for i in range((g+j)//2,n+1):
                l.append(i)
        else:
            for i in range((g+j)//2+1,n+1):
                l.append(i)
    print(len(l))
    print(*l)