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 bisect import bisect_left

def get(x, n):
    if x==n: return [1]
    return [a for i in range(x+1,n+1) for a in [x,i]]

def solve():
    n,l,r = map(int,input().split())
    cum = [0]*(n+1)
    for i in range(1,n):
        cum[i] = cum[i-1] + 2*(n-i)
    cum[n] = cum[n-1] + 1
    xL = bisect_left(cum, l)
    xR = bisect_left(cum, r)
    hL = l - cum[xL-1] - 1
    hR = r - cum[xR-1] - 1
    if xL==xR:
        u = get(xL, n)
        print(*u[hL:hR+1])
        return
    uL, uR = get(xL, n), get(xR, n)
    print(*uL[hL:], end=" ")
    for x in range(xL+1, xR):
        print(*get(x, n), end=" ")
    print(*uR[:hR+1])
    return

for _ in range(int(input())):
    solve()