Relatively Prime Graph CF1009D 暴力 思维

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 $\mathrm{G=(V,E)G=(V,E) relatively\; prime if\; and\; only\; if\; for\; each\; edge (v,u)\in E(v,u)\in E GCD(v,u)=1GCD(v,u)=1 (the\; greatest\; common\; divisor\; of vv and uu is 11).\; If\; there\; is\; no\; edge\; between\; some\; pair\; of\; vertices vv and uu then\; the\; value\; of GCD(v,u)GCD(v,u) doesn\text{'}t\; matter.\; The\; vertices\; are\; numbered\; from 11 to |V||V|.}$

Construct a relatively prime graph with $\mathrm{nn vertices\; and mm edges\; such\; that\; it\; is\; connected\; and\; it\; contains\; neither\; self-loops\; nor\; multiple\; edges.}$

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 $\mathrm{nn and mm (1\le n,m\le 1051\le n,m\le 105)\; —\; the\; number\; of\; vertices\; and\; the\; number\; of\; edges.}$

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 $\mathrm{ii-th\; of\; the\; next mm lines\; should\; contain\; the ii-th\; edge (vi,ui)(vi,ui) of\; the\; resulting\; graph\; (1\le vi,ui\le n,vi\ne ui1\le vi,ui\le n,vi\ne ui).\; For\; each\; pair (v,u)(v,u) there\; can\; be\; no\; more\; pairs (v,u)(v,u) or (u,v)(u,v).\; The\; vertices\; are\; numbered\; from 11 to nn.}$

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:

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;
}