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:
def main():
    t=int(input())
    for _ in range(t):
        n,l,r=map(int,input().split())
        if l==n*n-n+1:
            print(1)
            continue
        if r==n*n-n+1:
            r_g=n
        for i in range(n-1):
            if l>2*n-2-2*i:
                l-=2*n-2-2*i
            else:
                l_g=i+1
                break
        for i in range(n-1):
            if r>2*n-2-2*i:
                r-=2*n-2-2*i
            else:
                r_g=i+1
                break
        ans=[]
        for i in range(l_g,min(r_g+1,n)):
            for j in range(i+1,n+1):
                ans.append(i)
                ans.append(j)
        if r_g==n:
            ans.append(1)
        if r_g==n or r==2*n-2*r_g:
            print(*ans[l-1:])
        else:
            print(*ans[l-1:r+2*r_g-2*n])
if __name__ == '__main__':
    main()