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;
#define dhoom ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL);  
typedef long long ll;
typedef long double ld;
const ll inf = 1e18;
const int nax = 2e6 + 7;
const ll mod = 1e9 + 7;
//ll tree[4 * nax];
//9uS-22RSwk7gQqh

map< int , int > mp[nax];
int main()
{
	int n , m;
	cin >> n >> m;
	for(int i = 0 ; i < m ; i++){
		int u , v;
		cin >> u >> v;
		mp[u][v] = 1;
		mp[v][u] = 1;
	}
	for(int i = 2 ; i <= n - 1 ; i++){
			if(mp[1][i] == 1 && mp[i][n] == 1)
			{
				cout << "POSSIBLE" << endl;
				return 0;
			}
	}
	cout << "IMPOSSIBLE" << endl;
	return 0;
}