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: Wrong Answer)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
int cmp(const void*p,const void*q)
{
	return (*(int*)p-*(int*)q);
}
int a[300000],b[300000],c[300000],d[300000];
int main()
{
	int n,m,i,j,k,l,r,z; 
	scanf("%d%d",&n,&m);
	for(k=j=i=0;i<m;i++)
	{
		scanf("%d%d",&a[i],&b[i]);
		if(a[i]==1)
			c[j++]=b[i];
		if(b[i]==n)
			d[k++]=a[i];
	}
	if(c[0]!=0&&d[0]!=0)
	{
		qsort(c,j,sizeof(c[0]),cmp);
		qsort(d,j,sizeof(d[0]),cmp);
		for(z=i=0;i<=j;i++)
		{
			l=0;r=k;
			while(l<=r)
			{
				int m=(l+r)/2;
				if(d[m]<c[i])
					l=m+1;
				else if(d[m]>c[i])
					r=m-1;
				else
				{
					z=1;
					break;
				}
			}
		}
	}
	if(z)
		printf("POSSIBLE\n");
	else
		printf("IMPOSSIBLE\n");
	return 0;
}