Problem: You are given a complete directed graph K_n with n vertices: each pair of vertices u ≠ v in K_n have both directed edges (u, v) and (v, u); there are no self-loops.

You should find such a cycle in K_n that visits every directed edge exactly once (allowing for revisiting vertices).

We can write such cycle as a list of n(n - 1) + 1 vertices v_1, v_2, v_3, ..., v_{n(n - 1) - 1}, v_{n(n - 1)}, v_{n(n - 1) + 1} = v_1 — a visiting order, where each (v_i, v_{i + 1}) occurs exactly once.

Find the lexicographically smallest such cycle. It's not hard to prove that the cycle always exists.

Since the answer can be too large print its [l, r] segment, in other words, v_l, v_{l + 1}, ..., v_r.

Input

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

Next T lines contain test cases — one per line. The first and only line of each test case contains three integers n, l and r (2 ≤ n ≤ 10^5, 1 ≤ l ≤ r ≤ n(n - 1) + 1, r - l + 1 ≤ 10^5) — the number of vertices in K_n, and segment of the cycle to print.

It's guaranteed that the total sum of n doesn't exceed 10^5 and the total sum of r - l + 1 doesn't exceed 10^5.

Output

For each test case print the segment v_l, v_{l + 1}, ..., v_r of the lexicographically smallest cycle that visits every edge exactly once.

Example

Input


3
2 1 3
3 3 6
99995 9998900031 9998900031


Output


1 2 1 
1 3 2 3 
1 

Note

In the second test case, the lexicographically minimum cycle looks like: 1, 2, 1, 3, 2, 3, 1.

In the third test case, it's quite obvious that the cycle should start and end in vertex 1.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  std::ios::sync_with_stdio(false);
  cin.tie(0);
  int t;
  cin >> t;
  for (int tc = 0; tc < (t); tc += 1) {
    long long n, l, r;
    cin >> n >> l >> r;
    l--;
    bool last1 = false;
    if (r == n * (n - 1) + 1) {
      last1 = true;
      r--;
      if (r == l) {
        cout << "1\n";
        continue;
      }
    }
    long long i = 1;
    long long ptr = 0;
    while (ptr + (n - i) * 2 <= l) {
      ptr += (n - i) * 2;
      i++;
    }
    long long j = i;
    j += (l - ptr) / 2;
    if (l % 2 == 1) {
      cout << j + 1 << " ";
      j++;
      l++;
    }
    if (j != n) {
      j++;
    } else {
      i++;
      j = i + 1;
    }
    while (r > l) {
      if (r - l == 1) {
        cout << i << " ";
        break;
      }
      cout << i << " " << j << " ";
      if (j != n) {
        j++;
      } else {
        i++;
        j = i + 1;
      }
      r -= 2;
    }
    if (last1) cout << "1";
    cout << "\n";
  }
}