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:
for _ in range(int(input())):
    n, left, right = tuple(map(int, input().split()))
    maximal = n * (n - 1) + 1
    if left == maximal:
        print('1')
        continue
    if right == maximal:
        end_1 = True
    else:
        end_1 = False

    a = []
    summa = 0
    i = (n - 1) * 2
    cnt = 0
    while summa + i < left:
        summa += i
        i -= 2
        cnt += 1
    left -= summa
    right -= summa
    summa = 0

    # if cnt == 0:
    while left <= right:
        while left <= summa + i and left <= right:
            if left % 2 == 1:
                print(cnt + 1, end=' ')
            else:
                print(cnt + left // 2 + 1, end=' ')
            left += 1
        left -= i
        right -= i
        summa = 0
        i -= 2
        cnt += 1
        # print('!', i, sep='', end=' ')
        if i == 0 and end_1:
            print(1, end=' ')
            break
    print()
    # else:

    if left > right:
        continue

    # while left <= right:
    #     start =