Problem: You have a sequence a with n elements 1, 2, 3, ..., k - 1, k, k - 1, k - 2, ..., k - (n - k) (k ≤ n < 2k).

Let's call as inversion in a a pair of indices i < j such that a[i] > a[j].

Suppose, you have some permutation p of size k and you build a sequence b of size n in the following manner: b[i] = p[a[i]].

Your goal is to find such permutation p that the total number of inversions in b doesn't exceed the total number of inversions in a, and b is lexicographically maximum.

Small reminder: the sequence of k integers is called a permutation if it contains all integers from 1 to k exactly once.

Another small reminder: a sequence s is lexicographically smaller than another sequence t, if either s is a prefix of t, or for the first i such that s_i ≠ t_i, s_i < t_i holds (in the first position that these sequences are different, s has smaller number than t).

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

The first and only line of each test case contains two integers n and k (k ≤ n < 2k; 1 ≤ k ≤ 10^5) — the length of the sequence a and its maximum.

It's guaranteed that the total sum of k over test cases doesn't exceed 10^5.

Output

For each test case, print k integers — the permutation p which maximizes b lexicographically without increasing the total number of inversions.

It can be proven that p exists and is unique.

Example

Input


4
1 1
2 2
3 2
4 3


Output


1 
1 2 
2 1 
1 3 2 

Note

In the first test case, the sequence a = [1], there is only one permutation p = [1].

In the second test case, the sequence a = [1, 2]. There is no inversion in a, so there is only one permutation p = [1, 2] which doesn't increase the number of inversions.

In the third test case, a = [1, 2, 1] and has 1 inversion. If we use p = [2, 1], then b = [p[a[1]], p[a[2]], p[a[3]]] = [2, 1, 2] and also has 1 inversion.

In the fourth test case, a = [1, 2, 3, 2], and since p = [1, 3, 2] then b = [1, 3, 2, 3]. Both a and b have 1 inversion and b is the lexicographically maximum.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

#define lln long long int

#define fast ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);

void solve(){
	int n, k;
	cin>>n>>k;

	vector<int> a(n+1);

	for(int i = 1;i<=k;i++)
		a[i] = i;

	int x = k - 1;

	for(int i = k+1;i<=n;i++){
		a[i] = x;
		x--;
	}

	vector<int> p(n+1);
	vector<int> ans;

	for(int i = n;i>=1;i--){
		if(p[a[i]]==1)
			continue;
		else {
			ans.push_back(a[i]);
			p[a[i]] = 1;
		}
	}
	reverse(ans.begin(),ans.end());

	for(auto i:ans){
		cout<<i<<" ";
	}
	cout<<endl;
}

int main(){
    fast

    int q;
    cin>>q;

    while(q--){
		solve();
    }

	return 0;
}