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)

#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define ALL(x) (x).begin(), (x).end()
typedef long long ll;
typedef pair<int, int> P;
typedef vector<vector<int>> Matrix;
static const int INF = 2000000000;

vector<int> x, y;

bool isOK(vector<int> a, int index, int key){
  if(a[index] >= key) return true;
  else return false;
}

int binary_search(vector<int> a, int key){
  int ng = -1;
  int ok = (int)a.size();
  while(abs(ok - ng) > 1){
    int mid = (ok + ng) / 2;
    if(isOK(a, mid, key)) ok = mid;
    else ng = mid;
  }
  return ok;
}

int main(){
  int n, m;
  cin >> n >> m;
  rep(i, m){
    int a, b;
    cin >> a >> b;
    if (a == 1) x.push_back(b);
    else if (b == n) y.push_back(a);
  }
  x.push_back(20000000);
  sort(ALL(x));
  bool ok = false;
  rep(i, y.size()){
    int v = binary_search(x, y[i]);
    if (x[v] == y[i]) ok = true;
  }
  if (ok) cout << "POSSIBLE\n";
  else cout << "IMPOSSIBLE\n";
}