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 <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <vector>
#include <algorithm>
using namespace std;

const int MaxN = 400000;
int n, m;
vector <int> g[MaxN + 5];
bool vis[MaxN + 5];

int main()
{
	while (~scanf("%d%d", &n, &m)) {
		memset(vis, 0, sizeof(vis));
		for (int i = 1; i <= m; i++) {
			int u, v;
			scanf("%d%d", &u, &v);
			g[u].push_back(v);
			g[v].push_back(u);
		}
		for (int i = 0; i < g[1].size(); i++) vis[g[1][i]] = true;
		bool flag = false;
		for (int i = 0; i < g[n].size(); i++) 
			if (vis[g[n][i]]) flag = true;
		if (flag) printf("POSSIBLE\n"); else printf("IMPOSSIBLE\n");
	}
	return 0;
}