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"
#define rep(i,b) for(ll i=0;i<b;i++)
#define ll long long
using namespace std;
/*--Input//////////////////////////////////////////////////*/
inline void IN(void){return;}
template <typename First, typename... Rest>
void IN(First& first, Rest&... rest){cin >> first;IN(rest...);return;}
#define SS(T, ...)      T __VA_ARGS__; IN(__VA_ARGS__);
#define SV(type,c,n) vector<type> c(n);for(auto& i:c)cin >> i;
/*--Output/////////////////////////////////////////////////*/
inline int p(void){cout << endl; return 0;}
template<class Head> int p(Head&& head){cout << head;p();return 0;} template<class Head,class... Tail> int p(Head&& head,Tail&&... tail){cout<<head<<" ";p(forward<Tail>(tail)...);return 0;}
struct ProconInit {
    static constexpr bool AUTOFLUSH = false;
    ProconInit() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        if(AUTOFLUSH)
            cout << unitbuf;
    }
} PROCON_INIT;

#define YES(n) cout << ((n) ? "YES" : "NO"  ) << endl
#define Yes(n) cout << ((n) ? "Yes" : "No"  ) << endl
#define vl vector<ll>
#define vvl vector<vector<ll>>
#define vvvl vector<vector<vector<ll>>>
#define debug(x) cerr<<#x<<" "<<x<<'\n';
#define all(x) (x).begin(),(x).end()
#define bit(n) (1LL<<(n))
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
bool cmp(pair<ll,ll> a, pair<ll,ll> b) { return a.second < b.second; }

const int MOD = 1000000007;

const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};

signed main() {
    SS(ll,n,m);
    vector<bool>one(n);
    vector<bool>two(n);
    rep(i,m){
        SS(ll,v1,v2);
        v1--;v2--;
        if(v1==0)one[v2]=true;
        else if(v2==n-1)two[v1]=true;
    }
    rep(i,n){
        if(one[i]&&two[i]){
            p("POSSIBLE");
            return 0;
        }
    }
    p("IMPOSSIBLE");
}