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;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<vvll> vvvll;
typedef vector<string> vstr;
typedef pair<ll, ll> pll;
typedef vector<pll> vp;
typedef map<ll, ll> mll;
typedef map<string, ll> mstrll;
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fir first
#define sec second
#define maxs(x, y) (x = max(x, y))
#define mins(x, y) (x = min(x, y))
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define _overload3(_1, _2, _3, name, ...) name
#define _rep(i, n) repi(i, 0, n)
#define repi(i, a, b) for(ll i = ll(a); i < ll(b); i++)
#define rep(...) _overload3(__VA_ARGS__, repi, _rep,)(__VA_ARGS__)
#define each(i, n) for(auto&& i: n)
#define out(x) cout << (x)
#define print(x) cout << (x) << '\n'
#define debug(x) cerr << #x << ": " << (x) << '\n'
ll gcd(ll a, ll b){return b != 0 ? gcd(b, a % b) : a;}
ll lcm(ll a, ll b){return a * b / gcd(a, b);}
const ll INF = 1e16;
const ll MOD = 1e9 + 7;
ll a, b, c, n, m, x, y, z, w, h, ans, cnt, mx, mn;
string s, t;
vll dx = {-1, 0, 1, 0}, dy = {0, -1, 0, 1};
//vll dx = {-1, 0, 1, -1, 1, -1, 0, 1}, dy = {-1, -1, -1, 0, 0, 1, 1, 1};

signed main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    while(cin >> n >> m){
        vll from1, ton;
        rep(i, m){
            cin >> a >> b;
            if(a == 1 || b == 1){
                from1.pb(max(a, b));
            }else if(a == n || b == n){
                ton.pb(min(a, b));
            }
        }
        sort(all(ton));
        each(i, from1){
            if(binary_search(all(ton), i)){
                print("POSSIBLE");
                return 0;
            }
        }
        print("IMPOSSIBLE");
    }
}