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: Time Limit Exceeded)

#include<string>
#include<iostream>
#include<algorithm>
#include<set>
#include<math.h>
#include<vector>
#include<sstream>
#include<queue>
#include<functional>
#include<bitset>
#include<cstdio>
#include<iomanip>
#include<map>
#include<unordered_map>
#include<unordered_set>
#include <string.h>
using ll = long long;

#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define reps(i,x) for(int i=1;i<=(int)(x);i++)
#define rrep(i,x) for(int i=((int)(x)-1);i>=0;i--)
#define rreps(i,x) for(int i=((int)(x) - 1 * 100);i>0;i--)
#define all(x) (x).begin(),(x).end()
#define m0(x) memset(x,0,sizeof(x))
#define vll vector<ll>
#define vi vector<int>
#define mp make_pair
#define vpll vector<pair<ll,ll>>
#define vpi vector<pair<int,int>>

using namespace std;
int n, m;
int a[200000];
int b[200000];
int vstd[200000];
int main(void) {
	cin >> n >> m;
	vector<int> v;
	vector<int> v2;
	rep(i, m) {
		cin >> a[i] >> b[i];
		a[i];
		b[i];
		if (b[i] == n)
			v.push_back(a[i]);
		if (a[i] == 1)
			v2.push_back(b[i]);
	}
	for (auto e2 : v2) {
		if (find(all(v), e2) != v.end()) {
			cout << "POSSIBLE" << endl;
			return 0;
		}
	}
	cout << "IMPOSSIBLE" << endl;
	return 0;
}