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 "bits/stdc++.h"
using namespace std;
#define INF (1 << 29)

struct edge { int to, cost; };
typedef pair<int, int> P;   // firstは最短距離、secondは頂点の番号

const int MAX_V = 222222, MAX_E = 222222;

int V, E;
vector<edge> G[MAX_V];
int d[MAX_V];

bool dijkstra(int s) {
	// greater<P>を指定することでfirstが小さい順に取り出せるようにする
	priority_queue<P, vector<P>, greater<P> > que;
	fill(d, d + V, INF);
	d[s] = 0;
	que.push(P(0, s));

	while (!que.empty()) {
		P p = que.top(); que.pop();
		int v = p.second;
		if (d[v] < p.first) continue;
		for (int i = 0; i<G[v].size(); i++) {
			edge e = G[v][i];
			if (d[e.to] > d[v] + e.cost) {
				d[e.to] = d[v] + e.cost;
				que.push(P(d[e.to], e.to));
			}
		}
	}
	if(d[V-1]==2) return true;
	else return false;
}

int main() {
	cin >> V >> E;
	for (int i = 0; i < E; i++) {
		int s, t;
		cin >> s >> t;
		s--; t--;
		G[s].push_back(edge{ t,1 });
		G[t].push_back(edge{ s,1 });
	}
	cout << (dijkstra(0)?"POSSIBLE":"IMPOSSIBLE") << endl;
}