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: Wrong Answer)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)

using namespace std;
typedef long long int lli;
const int MAX = 200000;
int N, M;
//頂点数が多すぎるので隣接行列は使えない.代わりに隣接リストを使う
//Gは1と隣接,HはNと隣接
vector<bool> G(MAX,false), H(MAX,false);
int main() {
	cin >> N >> M;
	rep(i, M) {
		int s, t;
		cin >> s >> t;
		s--, t--;
		if (s == 0) G[t] = true;
		if (t == 0) G[s] = true;
		if (s == N-1) H[t] = true;
		if (t == N-1) H[s] = true;
	}
	//1とN以外の点を経由してNに着けるかをチェック
	bool vis = false;
	for (int v = 2;v <= N - 1;v++) {	
		if (G[v]&&H[v]) vis = true;
	}
	if (vis) cout << "POSSIBLE";
	else cout << "IMPOSSIBLE";
}