#include<bits/stdc++.h>
#define inf 1e9
#define eps 1e - 6
#define FOR(i, a, b) for(int i = a;i <= b;i ++)
#define REP(i, a, b) for(int i = a;i >= b;i --)
#define pa pair<int, int>
#define fr first
#define sd second
#define pb push_back
#define db double
#define MEM(a) memset(a, 0, sizeof(a))
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
inline ll read()
{
	char ch = getchar();
	ll s = 0, w = 1;
	while (ch < '0' || ch > '9') {if (ch == '-')w = -1; ch = getchar();}
	while (ch >= '0' && ch <= '9') {s = s * 10 + ch - '0'; ch = getchar();}
	return s * w;
}
#define N 500010
int n, m;
int a[N], b[N], p[N];
vector<int>e[N];
int vst[N], st[N], top;
int d[N], deg[N], dep[N];
int flag = 0;
int id[N];
inline void ck(vector<int> G)
{
	int tot = 0; int k = G.size();
	for (int x : G)id[x] = ++ tot;
	vector<int> vst(n+1, 0);
	FOR(i, 1, m)
	{
		int x = a[i], y = b[i];
		if ((!id[x]) && (!id[y])) {cout << "impossible\n"; exit(0);}
		else if (id[x] && id[y])
		{
			if (id[x] > id[y]) swap(x, y);
			if ((id[y] != id[x] + 1) && (id[y] != k || id[x] != 1) && (x != y)) {cout << "impossible\n"; exit(0);}
		}
		else 
		{
			if(id[x]) swap(x,y);
			if(vst[x]) {cout << "impossible\n"; exit(0);}
			vst[x] = 1;
		}
	}
	cout << "possible\n";
}
void dfs(int x, int fa)
{
	// cerr << "EE:" << x << '\n';
	dep[x] = dep[fa] + 1;
	st[++ top] = x; vst[x] = 1;
	for (int y : e[x]) if (y != fa)
		{
			if (vst[y])
			{
				if(dep[y] > dep[x]) continue;
				// cerr << "??:" << x << " " << y << endl;
				// FOR(i, 1, top) cerr << st[i] << ' '; cerr << '\n';
				vector<int> G;
				while (st[top] != y)
				{
					G.pb(st[top--]);
				}
				G.pb(y);
				ck(G); exit(0);
			}
			dfs(y, x);
		}
	top --;
}
int main()
{
	m = read(), n = read();
	FOR(i, 1, m)
	{
		a[i] = read(), b[i] = read();
		if (a[i] != b[i])e[a[i]].pb(b[i]), e[b[i]].pb(a[i]);
		else p[a[i]] = 1;
	}
	FOR(i, 1, n)if (!vst[i]) {dfs(i, 0);}
	FOR(i, 1, m)
	{
		if(a[i] != b[i]) deg[a[i]] ++, deg[b[i]] ++;
	}
	FOR(i, 1, n)d[i] = deg[i];
	FOR(i, 1, n)if(deg[i] == 1 && p[i] == 0)
	{
		for(int j : e[i]) d[j] --;
	}
	FOR(i, 1, n)if(d[i] > 2){cout << "impossible\n"; exit(0);}
	cout << "possible\n";
	return 0;
}