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 PYTHON3):

Solution:
from sys import *
t = int(stdin.readline())
import math
for _ in range(t):
    n,l,r = list(map(int,stdin.readline().split(' ')))
    
    if(l == n*n-n+1):
        print('1')
        continue
    k = math.ceil(((2*n-1) - math.sqrt((2*n-1)**2 - 4*l))/2)
    s = k*(2*n-1 -k)
    sl = 2*(n-k)
    lb = k
    eb = k+1+math.ceil((l-s+sl)/2)-1
    while(l <= r):
        if(l == n*n-n+1):
            break
        if(l%2 == 0):
            stdout.write(str(eb)+' ')
            eb = eb+1
            if(eb > n):
                lb = lb+1
                eb = lb+1
        else:
            stdout.write(str(lb)+' ')
        l = l+1
    if(r == n*n-n+1):
        stdout.write('1')
    stdout.write('\n')