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;

typedef pair<int, int> P_ii;
typedef pair<string, int> P_si;
typedef long long int ll;

const int MOD = 1000000007;

int main() {
    int N, M;
    cin >> N >> M;
    vector<vector<int> > Glaph(N+10);
    for (int j = 0; j < M; ++j) {
        int a, b;
        cin >> a >> b;
        Glaph[a].push_back(b);
        Glaph[b].push_back(a);
    }
    for (int i = 0; i < (int)Glaph[1].size(); ++i) {
        int from = Glaph[1][i];
        for (int j = 0; j < (int)Glaph[from].size(); ++j) {
            int to = Glaph[from][j];
            if (to == N) {
                printf("%s\n", "POSSIBLE");
                return 0;
            }
        }
    }
    printf("%s\n", "IMPOSSIBLE");
    return 0;
}