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> // cout, endl, cin
#include <string> // string, to_string, stoi
#include <vector> // vector
#include <algorithm> // min, max, swap, sort, reverse, lower_bound, upper_bound
#include <utility> // pair, make_pair
#include <tuple> // tuple, make_tuple
#include <cstdint> // int64_t, int*_t
#include <cstdio> // printf
#include <map> // map
#include <queue> // queue, priority_queue
#include <set> // set
#include <stack> // stack
#include <deque> // deque
#include <unordered_map> // unordered_map
#include <unordered_set> // unordered_set
#include <bitset> // bitset
#include <cctype> // isupper, islower, isdigit, toupper, tolower
#include <math.h>
#include <cstdlib>
#include <iomanip>
#define rep(i,x) for(ll i=0;i<x;i++)
#define all(a) (a).begin(),(a).end()
using namespace std;
using ld = long double;
using ll = long long;
const ll INF = 10010010010;
typedef pair<ll, ll> P;
using graph = vector<vector<ll>>;
const ll mod = 1000000007;
ll gcd(ll a, ll b) {//a>b
    if (a < b)swap(a, b);
    if (a % b == 0) return b;
    else return gcd(b, a % b);
}/*フィボナッチテンプレ
ll memo[50];
ll fibo(ll n) {
    if (memo[n] != 0)return memo[n];
    if (n <= 1)return memo[n] = n;
    else return memo[n] = fibo(n - 1) + fibo(n - 2);
}
*/
int main() {
    ll N, M;
    cin >> N >> M;
    graph G(N);
    ll a, b;
    rep(i, M) {
        cin >> a >> b;
        G[a - 1].push_back(b - 1);
        G[b - 1].push_back(a - 1);
    }
    bool ok = false;
    for (auto x : G[0]) {
        for (auto y : G[x]) {
            if (y + 1 == N)ok = true;
        }
    }
    if (ok)cout << "POSSIBLE" << endl;
    else cout << "IMPOSSIBLE" << endl;
}