Minimum Euler Cycle

You are given a complete directed graph $K_n$ with $n$ vertices: each pair of vertices $u \neq v$ 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 $v_1, v_2, v_3, \dots, v_{n(n – 1) – 1}, v_{n(n – 1)}, v_{n(n – 1) + 1} = v_1$ — 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, $v_l, v_{l + 1}, \dots, v_r$.

Input

The first line contains the single integer $T$ ($1 \le T \le 100$) — 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 $r$ ($2 \le n \le 10^5$, $1 \le l \le r \le n(n – 1) + 1$, $r – l + 1 \le 10^5$) — 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 $v_l, v_{l + 1}, \dots, v_r$ 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:

#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef long long ll;
typedef pair<int,int> PII;
typedef double db;
mt19937 mrand(random_device{}());
const ll mod=1000000007;
int rnd(int x) { return mrand() % x;}
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
// head

const int N=101000;
int _,n;
ll l,r,s[N];

int calc(ll x) {
if (x>s[n-1]) return 1;
auto a=lower_bound(s+1,s+n,x)-s;
int b=x-s[a-1];
if (b%2==1) return a;
else return b/2+a;
}

int main() {
for (scanf("%d",&_);_;_--) {
scanf("%d%lld%lld",&n,&l,&r);
rep(i,1,n+1) s[i]=s[i-1]+2*(n-i);
for (ll i=l;i<=r;i++)
		 	printf("%d ",calc(i));
		puts("");
	}
}