CodeForces 1009 D. Relatively Prime Graph（思维）

D. Relatively Prime Graph

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Let's call an undirected graph $G=(V,E)$ relatively prime if and only if for each edge $(v,u)\in E$  $GCD(v,u)=1$ (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 $1$ to $|V|$.

Construct a relatively prime graph with $n$ vertices and $m$ 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 $n$ and $m$ ($1\le n,m\le {10}^5$) — 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 $i$-th of the next $m$ lines should contain the $i$-th edge $(v_i,u_i)$ of the resulting graph ($1\le v_i,u_i\le n,v_i\ne u_i$). For each pair $(v,u)$ there can be no more pairs $(v,u)$ or $(u,v)$. The vertices are numbered from $1$ to $n$.

If there are multiple answers then print any of them.

Examples

input

Copy

5 6

output

Copy

Possible
2 5
3 2
5 1
3 4
4 1
5 4

input

Copy

6 12

output

Copy

Impossible

Note

Here is the representation of the graph from the first example:

#include<bits/stdc++.h>
using namespace std;
#define LL long long 


const int MAXN = 1e5+10;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9+7;
const int N = 1010;


int GCD(int a,int b){
	return b==0?a:GCD(b,a%b);
}
int n,m;
struct node{
	int u,v;
}p[MAXN];
int main(){
	while(scanf("%d%d",&n,&m)!=EOF){
		memset(p,0,sizeof(p));
		int num = 0;
		int flag = 0;
		for(int i=1;i<n;i++){
			for(int j=i+1;j<=n;j++){
				if(GCD(i,j)==1){
					if(num<m){
						p[num].u = i;p[num++].v = j;
					}
					else{
						break;
					}
				}
			}
		}
		if(num>=m&&m>=n-1){
			cout<<"Possible"<<endl;
			for(int i=0;i<m;i++){
				printf("%d %d\n",p[i].u,p[i].v);
			}
		}
		else cout<<"Impossible"<<endl;
	}
	return 0;
}