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 PYTHON):

Solution:
#####################################   
import atexit, io, sys, collections, math, heapq,fractions
buffer = io.BytesIO() 
sys.stdout = buffer
@atexit.register 
def write(): sys.__stdout__.write(buffer.getvalue())   
cookiejar = 1
#####################################

def f(n,k):
	p = range(k+1, n+1)
	cur = k/2 + (1 if k%2 == 1 else 0)
	while(cur < k):
		p.append(cur)
		cur+=1
	return p
nn = int(raw_input())
for i in range(nn):
	n,k = map(int,raw_input().split())
	p = f(n,k)
	print len(p)
	print ' '.join(map(str, p))