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 io,os
input=io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
import sys

def query(n,l,r):
    begin=1
    while l>(n-begin)*2+1:
        if begin==n:
            break
        l-=(n-begin)*2
        r-=(n-begin)*2
        begin+=1
    Ans=[]
    ans_l=0
    while ans_l<=r:
        if begin==n:
            Ans.append(1)
            break
        for j in range(begin+1,n+1):
            Ans.append(begin)
            Ans.append(j)
        ans_l+=(n-begin)*2
        begin+=1
    return Ans[l-1:r]

def main():
    t=int(input())
    for _ in range(t):
        n,l,r=map(int,input().split())
        Ans=query(n,l,r)
        sys.stdout.write(' '.join(map(str,Ans))+'\n')

if __name__=='__main__':
    main()