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: Wrong Answer)

/*
 ***
 Question Name:
 ***
 Question Link:
 
 ***
 Idea:
 */

#include <memory.h>
#include <iomanip>
#include <algorithm>
#include <iostream>
#include <iterator>
#include <numeric>
#include <sstream>
#include <fstream>
#include <cassert>
#include <climits>
#include <cstdlib>
#include <cstring>
#include <string>
#include <cstdio>
#include <vector>
#include <cmath>
#include <functional>
#include <queue>
#include <deque>
#include <stack>
#include <list>
#include <map>
#include <set>
#include <unordered_set>
#include <unordered_map>

#define REP(i,s,n) for(int (i)=s; (i)<(int)(n);(i)++)
#define RIT(it,c) for(__typeof(c.begin()) it = c.begin();it!=c.end();it++)
#define ALL(x) x.begin(), x.end()
#define SZ(x) (int)(x).size()
#define MSET(m,v) memset(m,v,sizeof(m))

using namespace std;

typedef long long LL;
typedef long double LD;
typedef vector<int> vi;
typedef pair<int,int> ii;
typedef vector<LL> vL;
typedef vector<bool> vb;
typedef unordered_set<int> ui;
typedef pair<LL,LL> pLL;

vector<vi> E;
int N,M;
int main(){
    cin>>N>>M;
    E.resize(N);
    for(int i=0;i<M;++i){
        int u,v;
        cin>>u>>v;
        E[u-1].push_back(v-1);
        E[v-1].push_back(u-1);
    }
    vb mark(N,true);
    queue<int> que;
    mark[0]=false;
    que.push(0);
    while(!que.empty()){
        int k = que.front();
        que.pop();
        for(auto j:E[k]) if(mark[j]){
            if(j==N-1){
                cout<<"POSSIBLE"<<endl;
                return 0;
            }
            mark[j] = false;
            que.push(j);
        }
    }
    cout<<"IMPOSSIBLE"<<endl;
    return 0;
}