Problem:
Score : 300 points

Problem Statement

In Takahashi Kingdom, there is an archipelago of N islands, called Takahashi Islands.
For convenience, we will call them Island 1, Island 2, ..., Island N.

There are M kinds of regular boat services between these islands.
Each service connects two islands. The i-th service connects Island a_i and Island b_i.

Cat Snuke is on Island 1 now, and wants to go to Island N.
However, it turned out that there is no boat service from Island 1 to Island N, so he wants to know whether it is possible to go to Island N by using two boat services.

Help him.

Constraints

3 ≤ N ≤ 200 000

1 ≤ M ≤ 200 000

1 ≤ a_i < b_i ≤ N

(a_i, b_i) \neq (1, N)

If i \neq j, (a_i, b_i) \neq (a_j, b_j).

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

If it is possible to go to Island N by using two boat services, print POSSIBLE; otherwise, print IMPOSSIBLE.

Sample Input 1

3 2
1 2
2 3

Sample Output 1

POSSIBLE

Sample Input 2

4 3
1 2
2 3
3 4

Sample Output 2

IMPOSSIBLE

You have to use three boat services to get to Island 4.

Sample Input 3

100000 1
1 99999

Sample Output 3

IMPOSSIBLE

Sample Input 4

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

Sample Output 4

POSSIBLE

You can get to Island 5 by using two boat services: Island 1 -> Island 4 -> Island 5.

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

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

#define ll long long
#define INF_LL 1LL << 60
#define INF 99999999
#define MOD (ll)1000000007
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define REP(i, a, n) for(int i = a; i < (int)(n); i++)
#define all(x) (x).begin(),(x).end()

void put_double(double obj){printf("%.12f\n",obj);};

template < typename T > std::string to_string( const T& n )
{
    std::ostringstream stm ;
    stm << n ;
    return stm.str() ;
}

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }

#define MAX_V (ll)1e5+1

struct edge {
    ll to;
    ll cost;
};

// <最短距離, 頂点の番号>
#define P pair<ll, ll>

// Vは頂点数
ll V;
vector<edge> G[MAX_V];
vector<ll> d(MAX_V, INF_LL);

void dijkstra(ll s) {
    priority_queue<P, vector<P>, greater<P> > que;
    d[s] = 0;
    que.push(P(0, s));

    while (!que.empty()) {
        P p = que.top();
        que.pop();
        ll v = p.second;
        if (d[v] < p.first) continue;

        for (ll i=0; i<G[v].size(); ++i) {
            edge e = G[v][i];
            if (d[e.to] > d[v] + e.cost) {
                d[e.to] = d[v] + e.cost;
                que.push(P(d[e.to], e.to));
            }
        }
    }
}


int main()
{
    ll N,M;
    cin >> N >> M;
    
    rep(i,M)
    {
        ll a,b;
        cin >> a >> b;
        edge e = {a, 1};
        G[b].push_back(e);
        e = {b, 1};
        G[a].push_back(e);
    }
    dijkstra(1);

    if( d[N] < 3 ) cout << "POSSIBLE" << endl;
    else cout << "IMPOSSIBLE" << endl;
}