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: Accepted)

#include <bits/stdc++.h>
 
using namespace std;
 
int main() {
    int n;
    int m;
    
    cin>>n>>m;
    
    unordered_multimap<int, int> e1;
    unordered_multimap<int, int> en;
    for(int i = 0 ; i < m ; i++)
    {
        int a,b;
        cin>>a>>b;
        if(a==1)  e1.insert(make_pair(a,b));
        if(b==1)  e1.insert(make_pair(b,a));
        if(a==n)  en.insert(make_pair(b,a));
        if(b==n)  en.insert(make_pair(a,b));
    }
    bool isfind = false;
    auto range_e1 = e1.equal_range(1);
    for(auto it = range_e1.first ; it != range_e1.second ; it++)
    {
        int x = it->second;
        if(en.find(x) != en.end())
        {
            isfind = true;
            break;
        }
    }
    
    if(isfind)
    {
        cout<<"POSSIBLE";
    }
    else
    {
        cout<<"IMPOSSIBLE";
    }
    return 0;
}