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: Runtime Error)

#include<iostream>
#include<set>
using namespace std;
int a[20000+50],b[20000+50];
set<int> tmp;
int main ()
{
	int i,n,m;
	while(scanf("%d",&n)!=EOF)
	{
		int t1,t2,flag=0,k=0;
		scanf("%d",&m);
		for(i=0;i<m;i++)
		{
			scanf("%d %d",&a[i],&b[i]);
			if(a[i]==1)
				tmp.insert(b[i]);	
			if(b[i]==1)
				tmp.insert(a[i]);	
		}		
		for(set<int>::iterator it=tmp.begin();it!=tmp.end();it++)
			for(i=0;i<m;i++)
			{
				if((a[i]==*it&&b[i]==n)||(a[i]==n&&b[i]==*it))
				{
					printf("POSSIBLE\n");
					flag++;
					break;
				}
			}
		if(flag==0)
			printf("IMPOSSIBLE\n");
	}
}