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;
#pragma GCC optimize("Ofast")
#pragma GCC optimize("no-stack-protector")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,popcnt,abm,mmx,tune=native")
const long long MOD = 998244353;
long long gcd(long long a, long long b) {
  if (a < b) {
    swap(a, b);
  }
  while (b != 0) {
    long long tmp = b;
    b = a % b;
    a = tmp;
  }
  return a;
}
signed main() {
  cin.tie(0);
  cout.tie(0);
  ios_base::sync_with_stdio(0);
  long long t = 1;
  cin >> t;
  while (t--) {
    long long n, l, r;
    cin >> n >> l >> r;
    l--;
    long long cur_plus = 0;
    long long org = (n - 1) * 2;
    long long prev_org = 0;
    while (org < l) {
      n--;
      prev_org = org;
      org += (n - 1) * 2;
      cur_plus++;
    }
    while (l < r) {
      if (l % 2 == 1) {
        cout << (l - prev_org) / 2 + 2 + cur_plus << ' ';
        l++;
      }
      for (l = l; l < r && l < org; l += 2) {
        cout << 1 + cur_plus << ' ';
        if (l + 1 < r) {
          cout << (l - prev_org) / 2 + 2 + cur_plus << ' ';
        }
      }
      n--;
      prev_org = org;
      org += (n - 1) * 2;
      if (n == 1 && l < r) {
        cout << 1 << ' ';
        break;
      }
      if (n == 1) {
        break;
      }
      cur_plus++;
    }
    cout << "\n" << endl;
  }
}