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>

#define MAX_M	( 200000 )

int pass[MAX_M + 1][2] = { 0 };
int start_flags[MAX_M + 1] = { 0 };
int end_flags[MAX_M + 1] = { 0 };

int main()
{
	int N, M;
	
	scanf( "%d %d", &N, &M );
	
	int is_no_start_point = 1;
	int is_no_end_point = 1;
	for ( int i = 0; i <= M; i++ )
	{
		fflush( stdin );
		scanf( "%d %d", &pass[i][0], &pass[i][1] );
		if ( pass[i][0] == 1 )
		{
			start_flags[i] = 1;
			is_no_start_point = 0;
		}
		if ( pass[i][1] == N )
		{
			end_flags[i] = 1;
			is_no_end_point = 0;
		}
	}
	
	if ( is_no_start_point || is_no_end_point )
	{
		printf( "IMPOSSIBLE\n" );
		return 0;
	}
	
	if ( ( N * ( N - 1 ) ) <= M )
	{
		printf( "POSSIBLE\n" );
		return 0;
	}
	
	
	int is_possible = 0;
	for( int start_pos = 0; start_pos <= M; start_pos++ )
	{
		if ( start_flags[start_pos] )
		{
			int via_point = pass[start_pos][1];
			for( int end_pos = 0; end_pos <= M; end_pos++ )
			{
				if ( end_flags[end_pos] )
				{
					if ( via_point == pass[end_pos][0] )
					{
						is_possible = 1;
						break;
					}
				}
			}
		}
	}
	
	
	if ( is_possible )
	{
		printf( "POSSIBLE\n" );
	}
	else
	{
		printf( "IMPOSSIBLE\n" );
	}
	
	return 0;
}