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:
import sys
input = sys.stdin.readline

def li():return [int(i) for i in input().rstrip('\n').split()]
def val():return int(input().rstrip('\n'))


for _ in range(val()):
    n,l,r = li()
    orig = r
    l -= 1
    r -= l


    currleft = 0
    curs = n - 1
    while curs and currleft + 2*curs <= l:
        currleft += 2*curs
        curs -= 1
    
    start = n - curs
    ans = []
    head = start
    l -= currleft

    last = head + 1
    half = 0
    while l:
        half = 1
        start = last
        last += 1
        l -= 1
        if not l:break
        half = 0
        start = head
        l -= 1

    if half:
        ans.append(start)
        if last == n + 1:
            head += 1
            last = head + 1
        start = head
        r -= 1

    while r:
        ans.append(start)
        r -= 1
        if not r:break
        start = last
        ans.append(start)
        last += 1
        if last == n + 1:
            head += 1
            last = head + 1
        r -= 1
        start = head
    
    if orig == n*(n-1) + 1:
        ans[-1] = 1

    print(*ans)