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:
def sieve():
    prime=[1]*1000005
    prime[0]=0
    prime[1]=0
    p=2
    while(p*p<1000005):
        if(prime[p]==1):
            for i in range(p*p,1000001,p):
                prime[i]=0
        p+=1
    return prime
def power(x, y):
    res = 1
    if (x == 0):
        return 0
    while (y > 0):
        if ((y & 1) == 1):
            res = (res * x)
        y //=2
        x *=x
    return res
for _ in range(int(input())):
    n,k=map(int,input().split())
    l=[]
    if(n>k):
        for i in range(k+1,n+1):
            l.append(i)
        for i in range((k+1)//2,k):
            l.append(i)
        print(len(l))
        print(*l)
    else:
        if(k==1 and n==1):
            print(0)
        else:
            for i in range((k+1)//2,k):
                l.append(i)
            print(len(l))
            print(*l)