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 int maxn = 3e5 + 9;
int main() {
  long long i, j, m, n, t, l, r, fir, sec;
  scanf("%lld", &t);
  while (t--) {
    scanf("%lld %lld %lld", &n, &l, &r);
    long long pos = 0;
    for (i = 1; i <= n; i++) {
      if (i == n) {
        pos = -1;
        break;
      }
      pos += (n - i) * 2;
      if (pos >= l) {
        pos -= (n - i) * 2 - 1;
        fir = i;
        break;
      }
    }
    if (pos == -1) {
      cout << 1 << endl;
      continue;
    }
    long long dis = l - pos + 1;
    sec = (dis + 1) / 2 + i;
    while (l <= r) {
      if (fir == n)
        printf("%lld", 1ll);
      else if (l % 2 == 1)
        printf("%lld", fir);
      else {
        printf("%lld", sec++);
        if (sec > n) {
          fir++;
          sec = fir + 1;
        }
      }
      printf("%c", l == r ? '\n' : ' ');
      l++;
    }
  }
  return 0;
}