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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
int comp(const void*a,const void*b)
{
	return *(int*)a-*(int*)b;
}
int main()
{
	int a[200001],b[200001];
	int x,y,n,t,m,j=0,k=0,i,p=0,l;
	scanf("%d %d",&n,&m);
	while(m--)
	{
		scanf("%d %d",&x,&y);
		if(x==1)
		{
			a[j]=y;
			j++;
		}
		if(y==n)
		{
			b[k]=x;
			k++;
		}
	}
	qsort(a,j,sizeof(a),comp);
	qsort(b,k,sizeof(b),comp);
	for(i=0;i<j;i++)
	{
		for(l=0;l<k;l++)
		{
			if(a[i]==b[l])
			{
				p=1;
				break;
			}
			if(a[i]<b[l])
			{
				i++;
			}
		}
	}
	if(p)
	{
		printf("POSSIBLE\n");
	}
	else
	{
		printf("IMPOSSIBLE\n");
	}
	return 0;
}