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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>

using namespace std;

int main(int argc, char const *argv[])
{
    int N, M;
    cin >> N >> M;
    vector<int> a, b;
    a.resize(M);
    b.resize(M);
    vector<bool> ftoi;
    vector<bool> itoN;
    ftoi.resize(N);
    itoN.resize(N);
    for (int i = 0; i < M; i++)
    {
        cin >> a[i];
        cin >> b[i];

        if (a[i] == 1)
        {
            ftoi[b[i] - 1] = true;
        }else
        {
            ftoi[b[i] - 1] = false;
        }
        if (b[i] == N)
        {
            itoN[a[i] - 1] = true;
        }else
        {
            itoN[a[i] - 1] = false;
        }
        
    }

    for (int i = 0; i < N; i++)
    {
        if (ftoi[i] & itoN[i])
        {
            cout << "POSSIBLE" << endl;
            return 0;
        }
        
    }
    
    cout << "IMPOSSIBLE" << endl;
    
    return 0;
}