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: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <iomanip>
#include <cstring>
#define rep(i, N) for (int i = 0; i < (int)N; i++)
using namespace std;
typedef long long ll;
const ll LLINF = 9223372036854775807;
const int MOD = 1000000007;

int main() {
  int N, M; cin >> N >> M;
  vector<vector<int>> ship(N+1);
  rep(i, M) {
    int a, b; cin >> a >> b;
    ship[a].push_back(b);
    ship[b].push_back(a);
  }

  vector<int> from_1 = ship[1], to_N = ship[N];
  string result = "IMPOSSIBLE";
  for (auto x: from_1) {
    if ( find(to_N.begin(), to_N.end(), x) != to_N.end() ) {
      result = "POSSIBLE";
    }
  }
  cout << result << endl;
  return 0;
}