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;

int main(){
        int N, M;
        cin>>N>>M;
        vector <int> st;
        vector <int> go;
        for(int i=0;i<M;i++){
                int a, b;
                cin>>a>>b;
                if(a==1)
                        st.push_back(b);
                if(b==N)
                        go.push_back(a);
        }
        sort(st.begin(), st.end());
        sort(go.begin(), go.end());
        bool res=false;
        int j=0, gosize=go.size();
        for(unsigned int i=0;i<st.size()&&!res;i++){
                for(;j<gosize&&go[j]<=st[i];j++){
                        if(st[i]==go[j]){
                                res=true;
                                break;
                        }
                }
                j--;
        }
        if(res)
                cout<<"POSSIBLE"<<endl;
        else
                cout<<"IMPOSSIBLE"<<endl;
        return 0;
}