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: Accepted)

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cstdlib>
#include <queue>

using namespace std;

const int N = 300000, M = 500000;

int d[N], used[N], S, T;
queue<int>Qe;

struct edge{
	edge *next,*other;
	int u,v,dis;
}e[M], *P=e, *point[N];

inline void add_edge(int x, int y, int dis)
{
	edge *Q = ++P;++P;
	P->u = x; P->v = y; P->next = point[x]; point[x]=P;
	Q->u = y; Q->v = x; Q->next = point[y]; point[y] = Q;
	P->dis = Q->dis = dis;
}

int SPFA()
{
	memset(d, 0x7f, sizeof(d));
	memset(used, 0, sizeof(used));
	
	Qe.push(S);
	used[S]=1; d[S]=0;
	
	while(!Qe.empty())
	{
		int x = Qe.front(); Qe.pop();
		used[x] = false;
		for(edge *j = point[x]; j; j=j->next)
		{
			if(d[x] + j->dis < d[j->v])
			{
				d[j->v] = d[x] + j->dis;
				if(!used[j->v])
				{
					used[j->v] = true; Qe.push(j->v);
				}
			}
		}
	}
	
	return d[T];
}

int n, s, t;

int main()
{
	int n,m,ts,te;
	scanf("%d%d", &n, &m);
	S = 1; T = n;
	for(int i = 1; i <= m; i++)
	{
		int a,b,c;scanf("%d%d", &a, &b);
		add_edge(a,b,1);
	}
	
	if(SPFA()==2)
		cout<<"POSSIBLE"<<endl;
	else
		cout<<"IMPOSSIBLE"<<endl;
}