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;
const long long mod = 998244353;
const int N = 2e5 + 2;
int main() {
  int t;
  scanf("%d", &t);
  while (t--) {
    long long n, l, r;
    scanf("%lld", &n);
    scanf("%lld", &l);
    scanf("%lld", &r);
    long long cur = 0, val = 2 * (n - 1), ind = 1;
    while (cur + val < l) {
      cur += val;
      val /= 2;
      val--;
      val *= 2;
      ind++;
      if (ind == n) val = 1;
    }
    long long total = n * (n - 1) + 1;
    long long ptr = cur + 1;
    long long x = ind, y = x + 1;
    vector<pair<long long, long long> > v;
    while (ptr <= r) {
      if (ptr == total) {
        v.push_back({1, ptr});
        break;
      }
      v.push_back({x, ptr});
      v.push_back({y, ptr + 1});
      ptr += 2;
      y++;
      if (y > n) {
        x++;
        y = x + 1;
        if (x == n) {
          v.push_back({1, ptr});
          break;
        }
      }
    }
    for (auto i : v)
      if (i.second >= l && i.second <= r) printf("%d ", (int)i.first);
    printf("\n");
  }
  return 0;
}