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: Time Limit Exceeded)

#pragma warning(disable:4996)
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#define MAX_STRING 20
#define MAXSHIPS 200000

	int aShipStart[MAXSHIPS];
	int aShipEnd[MAXSHIPS];

int main() {
	char sInput[MAX_STRING]="";
	char* psInput;
	int nMaxIsland=0;
	int nShipNumber=0;
	int nMiddleIsland=0;
	int i=0;
	int j=0;
	int nFind=0;
	
	// read line 1
	gets(sInput);
	psInput = strtok(sInput," ");
	nMaxIsland = atoi(psInput);
	psInput = strtok(NULL," ");
	nShipNumber = atoi(psInput);

	// read line 2
	for (i=0;i<nShipNumber;i++){
		gets(sInput);
		psInput = strtok(sInput," ");
		aShipStart[i] = atol(psInput);
		psInput = strtok(NULL," ");
		aShipEnd[i] = atol(psInput);
	}
	// search
	for (i=0;i<nShipNumber;i++){
		if (aShipStart[i]==1){
			nMiddleIsland = aShipEnd[i];
			for (j=0;j<nShipNumber;j++){
				if(aShipStart[j]==nMiddleIsland && aShipEnd[j]==nMaxIsland){
					 nFind=1;
					 break;
				}
			}
			if(nFind==1){
				break;
			}
		}
	}

	if (nFind==1){
		printf("POSSIBLE\n");
	} else {
		printf("IMPOSSIBLE\n");
	}

    return 0;
}