Relatively Prime Graph CF1009D 暴力思维

Let's call an undirected graph |V|.

Construct a relatively prime graph with 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 1≤n,m≤105) — 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 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: $Relatively Prime Graph CF1009D 暴力思维$

emmm，没想到直接暴力过了。。

直接暴力最大公约数为1的对数，当对数超过m直接break，没有时间超限

#include <map>
#include <set>
#include <stack>
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <string>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <algorithm>
#define debug(a) cout << #a << " " << a << endl
using namespace std;
const int maxn = 1e5 + 10;
const int mod = 1e9 + 7;
typedef long long ll;
vector< pair<ll,ll> > edge;
ll gcd( ll a, ll b ) {
    if( a == 0 ) {
        return b;
    } else if( b == 0 ) {
        return a;
    }
    return gcd( b, a%b );
}
int main() {
    ll n, m;
    cin >> n >> m;
    if( m < n-1 ) {
        cout << "Impossible" << endl;
    } else {
        for( ll i = 1; i < n; i ++ ) {
            for( ll j = i+1; j <= n; j ++ ) {
                if( gcd(i,j) == 1) {
                    edge.push_back(make_pair(i,j));
                    if( edge.size() > m ) {
                        break;
                    }
                }
            }
        }
        if( edge.size() < m ) {
            cout << "Impossible" << endl;
        } else {
            cout << "Possible" << endl;
            for( ll i = 0; i < m; i ++ ) {
                cout << edge[i].first << " " << edge[i].second << endl;
            }
        }
    }
    return 0;
}