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() {
  ios_base::sync_with_stdio(0);
  size_t T;
  cin >> T;
  while (T--) {
    long long int n, l, r;
    cin >> n >> l >> r;
    long long int t = 1;
    long long int k = 1;
    while (k < l && t != n) {
      k += 2 * (n - t++);
    }
    if (k > l) {
      k -= 2 * (n - --t);
    }
    if (t == n) {
      cout << 1 << endl;
      continue;
    }
    long long int difference = l - k;
    long long int c = difference / 2 + t + 1;
    if (difference % 2) {
      cout << c << " ";
      ++l;
      difference = l - k;
      c = difference / 2 + t + 1;
      if (c > n) {
        c = ++t + 1;
        if (t == n) {
          cout << 1 << endl;
          break;
        }
      }
    }
    if (difference % 2 == 0) {
      long long int current = l;
      while (current <= r) {
        cout << t << " ";
        ++current;
        if (current <= r) {
          cout << c++ << " ";
          ++current;
          if (c > n) {
            c = ++t + 1;
            if (t == n) {
              if (current <= r) cout << 1;
              break;
            }
          }
        }
      }
    }
    cout << endl;
  }
}