Let’s call an undirected graph G=(V,E)relatively prime if and only if for each edge (v,u)∈E GCD(v,u)=1 (the greatest common divisor of v and u is 1). If there is no edge between some pair of vertices v and u then the value of GCD(v,u) doesn’t matter. The vertices are numbered from 11 to |V|.
Construct a relatively prime graph with nn vertices and mm edges such that it is connected and it contains neither self-loops nor multiple edges.
If there exists no valid graph with the given number of vertices and edges then output “Impossible”.
If there are multiple answers then print any of them.
Input
The only line contains two integers nn and mm (1≤n,m≤10-5) — the number of vertices and the number of edges.
Output
If there exists no valid graph with the given number of vertices and edges then output “Impossible”.
Otherwise print the answer in the following format:
The first line should contain the word “Possible”.
The ii-th of the next mm lines should contain the ii-th edge (vi,ui) of the resulting graph (1≤vi,ui≤n,vi≠ui). For each pair (v,u) there can be no more pairs (v,u)or (u,v). The vertices are numbered from 11 to n.
If there are multiple answers then print any of them.
Examples
Input
5 6
Output
Possible
2 5
3 2
5 1
3 4
4 1
5 4
Input
6 12
Output
Impossible
Note
Here is the representation of the graph from the first example:
- 注意，因为m最大为1e5，因此直接暴力
#include<bits/stdc++.h>
#define endl '\n'
#define pb push_back
#define _ ios::sync_with_stdio(false)
#define mk make_pair
bool SUBMIT = 1;
typedef long long ll;
using namespace std;
const double PI = acos(-1);
const int inf = 1e5+50;
int n,m,k=0;
struct node{
int u,v;
node(int u,int v):u(u),v(v)
{}
};
vector<node>ans;
int main()
{
//if(!SUBMIT)freopen("i.txt","r",stdin);else _;
cin>>n>>m;
for(int i=1;i<n&&k<m;i++)
for(int j=i+1;j<=n&&k<m;j++)
if(__gcd(i,j)==1){
ans.pb(node(i,j));k++;
}
if(m<n-1||k<m){printf("Impossible\n");return 0;}
printf("Possible\n");
for(int i=0;i<ans.size();i++)
{
cout<<ans[i].u<<" "<<ans[i].v<<endl;
}
return 0;
}