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)

#include<iostream>
#include<vector>
#include<algorithm>
#include<cmath>
#include<set>

using namespace std;
using ll = long long;

int main() {
    int n,m,a,b;
    vector<int> from_one,to_n;

    cin >> n >> m;
    for(int i=0;i<m;i++){
        cin >> a >> b;
        if(a==1){
            from_one.push_back(b);
        }
        if(a==n){
            to_n.push_back(b);
        }
        if(b==n){
            to_n.push_back(a);
        }
    }
    sort(from_one.begin(),from_one.end());
    sort(to_n.begin(),to_n.end());
    int j=0;
    if(to_n.size()>0){
        for(int i=0;i<from_one.size();i++){
            while(j-1<to_n.size()&&from_one[i]<to_n[j])   j++;
            if(from_one[i]==to_n[j]){
                cout << "POSSIBLE";
                return 0;
            }
        }
    }
    cout << "IMPOSSIBLE";
	return 0;
}