Codeforces Round #351 Div. 2 D 贪心

D. Bear and Two Paths

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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.

题意：

有1-n个城市，有个人想从a到b城市，但是a到b没有直接相连的道路，所以他想经过所有城市1次后再到b，同样，c到的城市也是这样。a,b,c,d,四个城市是不同的。道路最多要k条，找出符合条件的两条路径。所有的路是双向的。

分析：

要想选择的路尽量的少，那么除了四个点之外的其他点要连在一起，这样最优。最少需要n+1条路。

如果有n=4，k<=n显然是不可以的。

#include<bits/stdc++.h>
using namespace std;
int main()
{
    int a,b,c,d,n,k;
    cin>>n>>k>>a>>b>>c>>d;
    if(n==4||k<=n){
        cout<<"-1";return 0;
    }
    cout<<a<<' '<<c;
    for(int i=1;i<=n;i++){
        if(i!=a&&i!=b&&i!=c&&i!=d)cout<<' '<<i;
    }
    cout<<' '<<d<<' '<<b<<endl;
    cout<<c<<' '<<a;
    for(int i=1;i<=n;i++)
        if(i!=a&&i!=b&&i!=c&&i!=d)cout<<' '<<i;
    cout<<' '<<b<<' '<<d<<endl;
    return 0;
}