VK Cup 2016 - Round 3 B. Counting Rhombi

Bearland has n cities, numbered 1 through n. Cities are connected via bidirectional roads. Each road connects two distinct cities. No two roads connect the same pair of cities.

Bear Limak was once in a city a and he wanted to go to a city b. There was no direct connection so he decided to take a long walk, visiting each city exactly once. Formally:

• There is no road between a and b.
• There exists a sequence (path) of n distinct cities v₁, v₂, ..., v_n that v₁ = a, v_n = b and there is a road between v_i and v_i + 1 for .

On the other day, the similar thing happened. Limak wanted to travel between a city c and a city d. There is no road between them but there exists a sequence of n distinct cities u₁, u₂, ..., u_n that u₁ = c, u_n = d and there is a road between u_i and u_i + 1 for .

Also, Limak thinks that there are at most k roads in Bearland. He wonders whether he remembers everything correctly.

Given n, k and four distinct cities a, b, c, d, can you find possible paths (v₁, ..., v_n) and (u₁, ..., u_n) to satisfy all the given conditions? Find any solution or print -1 if it's impossible.

Input

The first line of the input contains two integers n and k (4 ≤ n ≤ 1000, n - 1 ≤ k ≤ 2n - 2) — the number of cities and the maximum allowed number of roads, respectively.

The second line contains four distinct integers a, b, c and d (1 ≤ a, b, c, d ≤ n).

Output

Print -1 if it's impossible to satisfy all the given conditions. Otherwise, print two lines with paths descriptions. The first of these two lines should contain n distinct integers v₁, v₂, ..., v_n where v₁ = a and v_n = b. The second line should contain n distinct integers u₁, u₂, ..., u_n where u₁ = c and u_n = d.

Two paths generate at most 2n - 2 roads: (v₁, v₂), (v₂, v₃), ..., (v_n - 1, v_n), (u₁, u₂), (u₂, u₃), ..., (u_n - 1, u_n). Your answer will be considered wrong if contains more than k distinct roads or any other condition breaks. Note that (x, y) and (y, x) are the same road.

Examples

Input

7 11
2 4 7 3

Output

2 7 1 3 6 5 4
7 1 5 4 6 2 3

Input

1000 999
10 20 30 40

Output

-1

Note

In the first sample test, there should be 7 cities and at most 11 roads. The provided sample solution generates 10 roads, as in the drawing. You can also see a simple path of length n between 2 and 4, and a path between 7 and 3.

分析： k 小于 n+1时显然无解，其他情况下，把a,b放在头尾，cd分别放在第2和n-1的位置就行了。

#include <cstdio>
#include <iostream>
using namespace std;
int n,k,a,b,c,d,now,f[1001];
bool jud[1001];
int main()
{
	cin.sync_with_stdio(false);
	cin>>n>>k;
	cin>>a>>b>>c>>d;
	if(k < n + 1 || n == 4)
	{
		cout<<-1<<endl;
		return 0;		
	}
	f[1] = a;f[2] = c;f[n-1] = d;f[n] = b;
	jud[a] = jud[b] = jud[c] = jud[d] = true;
	int now = 1;
	for(int i = 3;i <= n-2;i++)
	{
		while(jud[now]) now++;
		f[i] = now;
		now++;
	}
	for(int i = 1;i <= n-1;i++) cout<<f[i]<<" ";
	cout<<f[n]<<endl;
	cout<<f[2]<<" "<<f[1]<<" ";
	for(int i = 3;i <= n-2;i++) cout<<f[i]<<" ";
	cout<<f[n]<<" "<<f[n-1];
}